pax_global_header 0000666 0000000 0000000 00000000064 13740675601 0014523 g ustar 00root root 0000000 0000000 52 comment=df9e869d31a5b8326a80d25c13b02b78cb1d3be8
pomegranate-0.13.5/ 0000775 0000000 0000000 00000000000 13740675601 0014113 5 ustar 00root root 0000000 0000000 pomegranate-0.13.5/.github/ 0000775 0000000 0000000 00000000000 13740675601 0015453 5 ustar 00root root 0000000 0000000 pomegranate-0.13.5/.github/ISSUE_TEMPLATE/ 0000775 0000000 0000000 00000000000 13740675601 0017636 5 ustar 00root root 0000000 0000000 pomegranate-0.13.5/.github/ISSUE_TEMPLATE/bug_report.md 0000664 0000000 0000000 00000001224 13740675601 0022327 0 ustar 00root root 0000000 0000000 ---
name: Bug report
about: Create a report to help us improve
title: "[BUG]"
labels: ''
assignees: ''
---
**Describe the bug**
A clear and concise description of what the bug is, including what you were expecting to happen and what actually happened. Please report the version of pomegranate that you are using and the operating system. Also, please make sure that you have upgraded to the latest version of pomegranate before submitting the bug report.
**To Reproduce**
Please provide a snippet of code that can reproduce this error. It is much easier for us to track down bugs and fix them if we have an example script that fails until we're successful.
pomegranate-0.13.5/.gitignore 0000664 0000000 0000000 00000000164 13740675601 0016104 0 ustar 00root root 0000000 0000000 *.pyc
*.c
.ipynb_checkpoints
*~
.DS_Store
build
*.so
.idea/
.vscode/
dist/
.eggs/
*.egg-info/
*.pyd
.python-version
pomegranate-0.13.5/.travis.yml 0000664 0000000 0000000 00000004257 13740675601 0016234 0 ustar 00root root 0000000 0000000 language: python
matrix:
include:
- services: docker
- os: osx
osx_image: xcode10.2
language: shell
env: PYTHON=3.6
- os: osx
osx_image: xcode10.2
language: shell
env: PYTHON=3.7
- os: osx
osx_image: xcode10.2
language: shell
env: PYTHON=3.8
- os: linux
language: generic
env: PYTHON=3.6
- os: linux
language: generic
env: PYTHON=3.7
- os: linux
language: generic
env: PYTHON=3.8
- os: windows
language: shell
before_install:
- choco install python --version 3.6.0
- export PATH="/c/Python36:/c/Python38/Scripts:$PATH"
# make sure it's on PATH as 'python3'
- ln -s /c/Python36/python.exe /c/Python36/python3.exe
- os: windows
language: shell
before_install:
- choco install python --version 3.7.0
- export PATH="/c/Python37:/c/Python37/Scripts:$PATH"
# make sure it's on PATH as 'python3'
- ln -s /c/Python37/python.exe /c/Python37/python3.exe
- os: windows
language: shell
before_install:
- choco install python --version 3.8.0
- export PATH="/c/Python38:/c/Python38/Scripts:$PATH"
# make sure it's on PATH as 'python3'
- ln -s /c/Python38/python.exe /c/Python38/python3.exe
before_install:
- if [[ "$TRAVIS_OS_NAME" == "osx" ]]; then wget http://repo.continuum.io/miniconda/Miniconda3-latest-MacOSX-x86_64.sh -O miniconda.sh;
else wget http://repo.continuum.io/miniconda/Miniconda3-latest-Linux-x86_64.sh -O miniconda.sh; fi
- bash miniconda.sh -b -p $HOME/miniconda
- export PATH="$HOME/miniconda/bin:$PATH"
- conda config --set always_yes yes --set changeps1 no
- conda update -q conda
- conda info -a
- conda create -q -n test-environment python=$PYTHON numpy scipy
- source activate test-environment
- pip install -r dev-requirements.txt
install:
- python -m pip install cibuildwheel==1.6.2
- python setup.py install
script:
- python setup.py test
- python -m cibuildwheel --output-dir wheelhouse
after_success:
# if the release was tagged, upload them to PyPI
- |
if [[ $TRAVIS_TAG ]]; then
python -m pip install twine
python -m twine upload wheelhouse/*.whl
fi
pomegranate-0.13.5/LICENSE 0000664 0000000 0000000 00000002073 13740675601 0015122 0 ustar 00root root 0000000 0000000 The MIT License (MIT)
Copyright (c) 2014 Jacob Schreiber
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.
pomegranate-0.13.5/MANIFEST 0000664 0000000 0000000 00000001533 13740675601 0015246 0 ustar 00root root 0000000 0000000 # file GENERATED by distutils, do NOT edit
CHANGES.txt
requirements.txt
setup.py
pomegranate/BayesClassifier.c
pomegranate/BayesClassifier.pyx
pomegranate/BayesianNetwork.c
pomegranate/BayesianNetwork.pyx
pomegranate/FactorGraph.c
pomegranate/FactorGraph.pyx
pomegranate/MarkovChain.c
pomegranate/MarkovChain.pyx
pomegranate/NaiveBayes.c
pomegranate/NaiveBayes.pyx
pomegranate/__init__.py
pomegranate/__init__.pyc
pomegranate/base.c
pomegranate/base.pxd
pomegranate/base.pyx
pomegranate/bayes.c
pomegranate/bayes.pxd
pomegranate/bayes.pyx
pomegranate/distributions.c
pomegranate/distributions.pxd
pomegranate/distributions.pyx
pomegranate/gmm.c
pomegranate/gmm.pyx
pomegranate/hmm.c
pomegranate/hmm.pyx
pomegranate/kmeans.c
pomegranate/kmeans.pyx
pomegranate/parallel.c
pomegranate/parallel.pyx
pomegranate/utils.c
pomegranate/utils.pxd
pomegranate/utils.pyx
pomegranate-0.13.5/MANIFEST.in 0000664 0000000 0000000 00000000137 13740675601 0015652 0 ustar 00root root 0000000 0000000 include *.txt
include LICENSE
graft tests
recursive-include pomegranate *.py *.c *.pxd *.pyx
pomegranate-0.13.5/Makefile 0000664 0000000 0000000 00000005324 13740675601 0015557 0 ustar 00root root 0000000 0000000 PACKAGE_NAME=pomegranate
PY2_ENV=py2.7
PY3_ENV=py3.6
default:
echo no default
.PHONY: install test bigclean nbtest nbclean
.PHONY: bigbuild py2build py3build
.PHONY: biginstall py2install py3install
.PHONY: biguninstall py2uninstall py3uninstall
.PHONY: bigtest py2test py3test
.PHONY: bignbtest py2nbtest py3nbtest
install:
python setup.py install
test:
python setup.py test
bigclean: nbclean
rm -rf build
rm -rf dist
rm -rf .eggs
rm -rf $(PACKAGE_NAME).egg-info
find . -name '*.pyc' -print | xargs rm
find . -name '*.so' -print | xargs rm
ifndef NO_REMOVE_CFILES
find . -name '*.c' -print | xargs rm
endif
# Add python dependencies
ifdef PY2_ENV
bigbuild: py2build
biginstall: py2install
biguninstall: py2uninstall
bigtest: py2test
bignbtest: py2test
endif
ifdef PY3_ENV
bigbuild: py3build
biginstall: py3install
biguninstall: py3uninstall
bigtest: py3test
# Don't know how to override the kernelspec and the notebooks are python2 only anyway
# bignbtest: py3test
endif
py2build:
(source activate $(PY2_ENV) ; python setup.py build ; python setup.py build_ext --inplace )
py3build:
(source activate $(PY3_ENV) ; python setup.py build ; python setup.py build_ext --inplace )
py2install:
(source activate $(PY2_ENV) ; python setup.py install )
py3install:
(source activate $(PY3_ENV) ; python setup.py install )
py3uninstall:
rm -rf ~/miniconda2/envs/$(PY3_ENV)/lib/python3.6/site-packages/$(PACKAGE_NAME)*
py2uninstall:
rm -rf ~/miniconda2/envs/$(PY2_ENV)/lib/python2.7/site-packages/$(PACKAGE_NAME)*
py3test:
(source activate $(PY3_ENV) ; python setup.py test )
py2test:
(source activate $(PY2_ENV) ; python setup.py test )
## Notebook tests
PYTHON_NOTEBOOKS= examples/*.ipynb tutorials/*.ipynb benchmarks/*.ipynb
EXECUTE_TIMEOUT=600
ALLOW_ERRORS=
# Allow errors if you want to check as many cells as possible
#ALLOW_ERRORS=--allow-errors
# Required conda package installs:
# CONDA_INSTALL_BASE_PACKAGES=cython scipy scikit-learn pandas joblib nose networkx=1.11
# CONDA_INSTALL_NOTEBOOK_PACKAGES=jupyter jupyter_contrib_nbextensions jupyter_nbextensions_configurator seaborn xlrd pygraphviz pillow
nbtest:
for nb in $(PYTHON_NOTEBOOKS) ; do time jupyter nbconvert $$nb --execute --ExecutePreprocessor.timeout=$(EXECUTE_TIMEOUT) --to html $(ALLOW_ERRORS) ; done
py2nbtest:
(source activate $(PY2_ENV) ; for nb in $(PYTHON_NOTEBOOKS) ; do time jupyter nbconvert $$nb --execute --ExecutePreprocessor.timeout=$(EXECUTE_TIMEOUT) --to html $(ALLOW_ERRORS) ; done )
py3nbtest:
(source activate $(PY3_ENV) ; for nb in $(PYTHON_NOTEBOOKS) ; do time jupyter nbconvert $$nb --execute --ExecutePreprocessor.timeout=$(EXECUTE_TIMEOUT) --to html $(ALLOW_ERRORS) ; done )
nbclean:
for nb in $(PYTHON_NOTEBOOKS) ; do rm -f $${nb%%.ipynb}.html ; done
pomegranate-0.13.5/README.md 0000664 0000000 0000000 00000011675 13740675601 0015404 0 ustar 00root root 0000000 0000000
[](https://travis-ci.org/jmschrei/pomegranate)  [](http://pomegranate.readthedocs.io/en/latest/?badge=latest) [](https://mybinder.org/v2/gh/jmschrei/pomegranate/master)
Please consider citing the [**JMLR-MLOSS Manuscript**](http://jmlr.org/papers/volume18/17-636/17-636.pdf) if you've used pomegranate in your academic work!
pomegranate is a package for building probabilistic models in Python that is implemented in Cython for speed. A primary focus of pomegranate is to merge the easy-to-use API of scikit-learn with the modularity of probabilistic modeling to allow users to specify complicated models without needing to worry about implementation details. The models implemented here are built from the ground up with big data processing in mind and so natively support features like multi-threaded parallelism and out-of-core processing. Click on the binder badge above to interactively play with the tutorials!
### Installation
pomegranate is pip-installable using `pip install pomegranate` and conda-installable using `conda install pomegranate`. If neither work, more detailed installation instructions can be found [here](http://pomegranate.readthedocs.io/en/latest/install.html).
### Models
* [Probability Distributions](http://pomegranate.readthedocs.io/en/latest/Distributions.html)
* [General Mixture Models](http://pomegranate.readthedocs.io/en/latest/GeneralMixtureModel.html)
* [Hidden Markov Models](http://pomegranate.readthedocs.io/en/latest/HiddenMarkovModel.html)
* [Naive Bayes and Bayes Classifiers](http://pomegranate.readthedocs.io/en/latest/NaiveBayes.html)
* [Markov Chains](http://pomegranate.readthedocs.io/en/latest/MarkovChain.html)
* [Discrete Bayesian Networks](http://pomegranate.readthedocs.io/en/latest/BayesianNetwork.html)
* [Discrete Markov Networks](https://pomegranate.readthedocs.io/en/latest/MarkovNetwork.html)
The discrete Bayesian networks also support novel work on structure learning in the presence of constraints through a constraint graph. These constraints can dramatically speed up structure learning through the use of loose general prior knowledge, and can frequently make the exact learning task take only polynomial time instead of exponential time. See the [PeerJ manuscript](https://peerj.com/articles/cs-122/) for the theory and the [pomegranate tutorial](https://github.com/jmschrei/pomegranate/blob/master/tutorials/B_Model_Tutorial_4b_Bayesian_Network_Structure_Learning.ipynb) for the practical usage!
To support the above algorithms, it has efficient implementations of the following:
* Kmeans/Kmeans++/Kmeans||
* Factor Graphs
### Features
* [sklearn-like API](https://pomegranate.readthedocs.io/en/latest/api.html)
* [Multi-threaded Training](http://pomegranate.readthedocs.io/en/latest/parallelism.html)
* [BLAS/GPU Acceleration](http://pomegranate.readthedocs.io/en/latest/gpu.html)
* [Out-of-Core Learning](http://pomegranate.readthedocs.io/en/latest/ooc.html)
* [Data Generators and IO](https://pomegranate.readthedocs.io/en/latest/io.html)
* [Semi-supervised Learning](http://pomegranate.readthedocs.io/en/latest/semisupervised.html)
* [Missing Value Support](http://pomegranate.readthedocs.io/en/latest/nan.html)
* [Customized Callbacks](http://pomegranate.readthedocs.io/en/latest/callbacks.html)
Please take a look at the [tutorials folder](https://github.com/jmschrei/pomegranate/tree/master/tutorials), which includes several tutorials on how to effectively use pomegranate!
See [the website](http://pomegranate.readthedocs.org/en/latest/) for extensive documentation, API references, and FAQs about each of the models and supported features.
No good project is done alone, and so I'd like to thank all the previous contributors to YAHMM, and all the current contributors to pomegranate, including the graduate students who share my office I annoy on a regular basis by bouncing ideas off of.
### Dependencies
pomegranate requires:
```
- Cython (only if building from source)
- NumPy
- SciPy
- NetworkX
- joblib
```
To run the tests, you also must have `nose` installed.
## Contributing
If you would like to contribute a feature then fork the master branch (fork the release if you are fixing a bug). Be sure to run the tests before changing any code. You'll need to have [nosetests](https://github.com/nose-devs/nose) installed. The following command will run all the tests:
```
python setup.py test
```
Let us know what you want to do just in case we're already working on an implementation of something similar. This way we can avoid any needless duplication of effort. Also, please don't forget to add tests for any new functions.
pomegranate-0.13.5/appveyor.yml 0000664 0000000 0000000 00000007317 13740675601 0016513 0 ustar 00root root 0000000 0000000 environment:
global:
# SDK v7.0 MSVC Express 2008's SetEnv.cmd script will fail if the
# /E:ON and /V:ON options are not enabled in the batch script intepreter
# See: http://stackoverflow.com/a/13751649/163740
CMD_IN_ENV: "cmd /E:ON /V:ON /C .\\appveyor\\run_with_env.cmd"
password:
secure: P2e7kP/2kOXij6nJNO75wA==
matrix:
# Pre-installed Python versions, which Appveyor may upgrade to
# a later point release.
# See: http://www.appveyor.com/docs/installed-software#python
- PYTHON: "C:\\Python36"
PYTHON_VERSION: "3.6"
PYTHON_ARCH: "32"
MINICONDA: C:\Miniconda3
- PYTHON: "C:\\Python36-x64"
PYTHON_VERSION: "3.6"
PYTHON_ARCH: "64"
MINICONDA: C:\Miniconda3-x64
- PYTHON: "C:\\Python37"
PYTHON_VERSION: "3.7"
PYTHON_ARCH: "32"
MINICONDA: C:\Miniconda3
- PYTHON: "C:\\Python37-x64"
PYTHON_VERSION: "3.7"
PYTHON_ARCH: "64"
MINICONDA: C:\Miniconda3-x64
- PYTHON: "C:\\Python38-x64"
PYTHON_VERSION: "3.8"
PYTHON_ARCH: "64"
MINICONDA: C:\Miniconda3-x64
install:
# If there is a newer build queued for the same PR, cancel this one.
# The AppVeyor 'rollout builds' option is supposed to serve the same
# purpose but it is problematic because it tends to cancel builds pushed
# directly to master instead of just PR builds (or the converse).
# credits: JuliaLang developers.
- ps: if ($env:APPVEYOR_PULL_REQUEST_NUMBER -and $env:APPVEYOR_BUILD_NUMBER -ne ((Invoke-RestMethod `
https://ci.appveyor.com/api/projects/$env:APPVEYOR_ACCOUNT_NAME/$env:APPVEYOR_PROJECT_SLUG/history?recordsNumber=50).builds | `
Where-Object pullRequestId -eq $env:APPVEYOR_PULL_REQUEST_NUMBER)[0].buildNumber) { `
throw "There are newer queued builds for this pull request, failing early." }
- ECHO "Filesystem root:"
- ps: "ls \"C:/\""
- ECHO "Installed SDKs:"
- ps: "ls \"C:/Program Files/Microsoft SDKs/Windows\""
# Install Python (from the official .msi of http://python.org) and pip when
# not already installed.
- ps: if (-not(Test-Path($env:PYTHON))) { & appveyor\install.ps1 }
# Prepend newly installed Python to the PATH of this build (this cannot be
# done from inside the powershell script as it would require to restart
# the parent CMD process).
- "set PATH=%MINICONDA%;%MINICONDA%\\Scripts;%PATH%"
- conda config --set always_yes yes --set changeps1 no
- conda update -q conda
# We need to install numpy, scipy and matplotlib through conda
- "conda create -q -n test-environment python=%PYTHON_VERSION% numpy scipy"
- activate test-environment
# Upgrade to the latest version of pip to avoid it displaying warnings
# about it being out of date.
- "pip install --disable-pip-version-check --user --upgrade pip"
# Install the build dependencies of the project. If some dependencies contain
# compiled extensions and are not provided as pre-built wheel packages,
# pip will build them from source using the MSVC compiler matching the
# target Python version and architecture
- "%CMD_IN_ENV% pip install -r dev-requirements.txt"
- "%CMD_IN_ENV% pip install twine"
build_script:
# Build the compiled extension
- "%CMD_IN_ENV% python setup.py build"
test_script:
# Run the project tests
- "%CMD_IN_ENV% python setup.py test"
after_test:
# If tests are successful, create binary packages for the project.
- "%CMD_IN_ENV% python setup.py bdist_wheel"
- ps: "ls dist"
artifacts:
# Archive the generated packages in the ci.appveyor.com build report.
- path: dist\*
deploy_script:
- if "%APPVEYOR_REPO_TAG%"=="true" ( twine upload -u jmschreiber -p %password% --skip-existing dist/* ) else ( echo "Not deplaying because not a tagged commit.")
pomegranate-0.13.5/appveyor/ 0000775 0000000 0000000 00000000000 13740675601 0015760 5 ustar 00root root 0000000 0000000 pomegranate-0.13.5/appveyor/install.ps1 0000664 0000000 0000000 00000016033 13740675601 0020056 0 ustar 00root root 0000000 0000000 # Sample script to install Python and pip under Windows
# Authors: Olivier Grisel, Jonathan Helmus, Kyle Kastner, and Alex Willmer
# License: CC0 1.0 Universal: http://creativecommons.org/publicdomain/zero/1.0/
$MINICONDA_URL = "http://repo.continuum.io/miniconda/"
$BASE_URL = "https://www.python.org/ftp/python/"
$GET_PIP_URL = "https://bootstrap.pypa.io/get-pip.py"
$GET_PIP_PATH = "C:\get-pip.py"
$PYTHON_PRERELEASE_REGEX = @"
(?x)
(?\d+)
\.
(?\d+)
\.
(?\d+)
(?[a-z]{1,2}\d+)
"@
function Download ($filename, $url) {
$webclient = New-Object System.Net.WebClient
$basedir = $pwd.Path + "\"
$filepath = $basedir + $filename
if (Test-Path $filename) {
Write-Host "Reusing" $filepath
return $filepath
}
# Download and retry up to 3 times in case of network transient errors.
Write-Host "Downloading" $filename "from" $url
$retry_attempts = 2
for ($i = 0; $i -lt $retry_attempts; $i++) {
try {
$webclient.DownloadFile($url, $filepath)
break
}
Catch [Exception]{
Start-Sleep 1
}
}
if (Test-Path $filepath) {
Write-Host "File saved at" $filepath
} else {
# Retry once to get the error message if any at the last try
$webclient.DownloadFile($url, $filepath)
}
return $filepath
}
function ParsePythonVersion ($python_version) {
if ($python_version -match $PYTHON_PRERELEASE_REGEX) {
return ([int]$matches.major, [int]$matches.minor, [int]$matches.micro,
$matches.prerelease)
}
$version_obj = [version]$python_version
return ($version_obj.major, $version_obj.minor, $version_obj.build, "")
}
function DownloadPython ($python_version, $platform_suffix) {
$major, $minor, $micro, $prerelease = ParsePythonVersion $python_version
if (($major -le 2 -and $micro -eq 0) `
-or ($major -eq 3 -and $minor -le 2 -and $micro -eq 0) `
) {
$dir = "$major.$minor"
$python_version = "$major.$minor$prerelease"
} else {
$dir = "$major.$minor.$micro"
}
if ($prerelease) {
if (($major -le 2) `
-or ($major -eq 3 -and $minor -eq 1) `
-or ($major -eq 3 -and $minor -eq 2) `
-or ($major -eq 3 -and $minor -eq 3) `
) {
$dir = "$dir/prev"
}
}
if (($major -le 2) -or ($major -le 3 -and $minor -le 4)) {
$ext = "msi"
if ($platform_suffix) {
$platform_suffix = ".$platform_suffix"
}
} else {
$ext = "exe"
if ($platform_suffix) {
$platform_suffix = "-$platform_suffix"
}
}
$filename = "python-$python_version$platform_suffix.$ext"
$url = "$BASE_URL$dir/$filename"
$filepath = Download $filename $url
return $filepath
}
function InstallPython ($python_version, $architecture, $python_home) {
Write-Host "Installing Python" $python_version "for" $architecture "bit architecture to" $python_home
if (Test-Path $python_home) {
Write-Host $python_home "already exists, skipping."
return $false
}
if ($architecture -eq "32") {
$platform_suffix = ""
} else {
$platform_suffix = "amd64"
}
$installer_path = DownloadPython $python_version $platform_suffix
$installer_ext = [System.IO.Path]::GetExtension($installer_path)
Write-Host "Installing $installer_path to $python_home"
$install_log = $python_home + ".log"
if ($installer_ext -eq '.msi') {
InstallPythonMSI $installer_path $python_home $install_log
} else {
InstallPythonEXE $installer_path $python_home $install_log
}
if (Test-Path $python_home) {
Write-Host "Python $python_version ($architecture) installation complete"
} else {
Write-Host "Failed to install Python in $python_home"
Get-Content -Path $install_log
Exit 1
}
}
function InstallPythonEXE ($exepath, $python_home, $install_log) {
$install_args = "/quiet InstallAllUsers=1 TargetDir=$python_home"
RunCommand $exepath $install_args
}
function InstallPythonMSI ($msipath, $python_home, $install_log) {
$install_args = "/qn /log $install_log /i $msipath TARGETDIR=$python_home"
$uninstall_args = "/qn /x $msipath"
RunCommand "msiexec.exe" $install_args
if (-not(Test-Path $python_home)) {
Write-Host "Python seems to be installed else-where, reinstalling."
RunCommand "msiexec.exe" $uninstall_args
RunCommand "msiexec.exe" $install_args
}
}
function RunCommand ($command, $command_args) {
Write-Host $command $command_args
Start-Process -FilePath $command -ArgumentList $command_args -Wait -Passthru
}
function InstallPip ($python_home) {
$pip_path = $python_home + "\Scripts\pip.exe"
$python_path = $python_home + "\python.exe"
if (-not(Test-Path $pip_path)) {
Write-Host "Installing pip..."
$webclient = New-Object System.Net.WebClient
$webclient.DownloadFile($GET_PIP_URL, $GET_PIP_PATH)
Write-Host "Executing:" $python_path $GET_PIP_PATH
& $python_path $GET_PIP_PATH
} else {
Write-Host "pip already installed."
}
}
function DownloadMiniconda ($python_version, $platform_suffix) {
if ($python_version -eq "3.4") {
$filename = "Miniconda3-3.5.5-Windows-" + $platform_suffix + ".exe"
} else {
$filename = "Miniconda-3.5.5-Windows-" + $platform_suffix + ".exe"
}
$url = $MINICONDA_URL + $filename
$filepath = Download $filename $url
return $filepath
}
function InstallMiniconda ($python_version, $architecture, $python_home) {
Write-Host "Installing Python" $python_version "for" $architecture "bit architecture to" $python_home
if (Test-Path $python_home) {
Write-Host $python_home "already exists, skipping."
return $false
}
if ($architecture -eq "32") {
$platform_suffix = "x86"
} else {
$platform_suffix = "x86_64"
}
$filepath = DownloadMiniconda $python_version $platform_suffix
Write-Host "Installing" $filepath "to" $python_home
$install_log = $python_home + ".log"
$args = "/S /D=$python_home"
Write-Host $filepath $args
Start-Process -FilePath $filepath -ArgumentList $args -Wait -Passthru
if (Test-Path $python_home) {
Write-Host "Python $python_version ($architecture) installation complete"
} else {
Write-Host "Failed to install Python in $python_home"
Get-Content -Path $install_log
Exit 1
}
}
function InstallMinicondaPip ($python_home) {
$pip_path = $python_home + "\Scripts\pip.exe"
$conda_path = $python_home + "\Scripts\conda.exe"
if (-not(Test-Path $pip_path)) {
Write-Host "Installing pip..."
$args = "install --yes pip"
Write-Host $conda_path $args
Start-Process -FilePath "$conda_path" -ArgumentList $args -Wait -Passthru
} else {
Write-Host "pip already installed."
}
}
function main () {
InstallPython $env:PYTHON_VERSION $env:PYTHON_ARCH $env:PYTHON
InstallPip $env:PYTHON
}
main
pomegranate-0.13.5/appveyor/run_with_env.cmd 0000664 0000000 0000000 00000006446 13740675601 0021166 0 ustar 00root root 0000000 0000000 :: To build extensions for 64 bit Python 3, we need to configure environment
:: variables to use the MSVC 2010 C++ compilers from GRMSDKX_EN_DVD.iso of:
:: MS Windows SDK for Windows 7 and .NET Framework 4 (SDK v7.1)
::
:: To build extensions for 64 bit Python 2, we need to configure environment
:: variables to use the MSVC 2008 C++ compilers from GRMSDKX_EN_DVD.iso of:
:: MS Windows SDK for Windows 7 and .NET Framework 3.5 (SDK v7.0)
::
:: 32 bit builds, and 64-bit builds for 3.5 and beyond, do not require specific
:: environment configurations.
::
:: Note: this script needs to be run with the /E:ON and /V:ON flags for the
:: cmd interpreter, at least for (SDK v7.0)
::
:: More details at:
:: https://github.com/cython/cython/wiki/64BitCythonExtensionsOnWindows
:: http://stackoverflow.com/a/13751649/163740
::
:: Author: Olivier Grisel
:: License: CC0 1.0 Universal: http://creativecommons.org/publicdomain/zero/1.0/
::
:: Notes about batch files for Python people:
::
:: Quotes in values are literally part of the values:
:: SET FOO="bar"
:: FOO is now five characters long: " b a r "
:: If you don't want quotes, don't include them on the right-hand side.
::
:: The CALL lines at the end of this file look redundant, but if you move them
:: outside of the IF clauses, they do not run properly in the SET_SDK_64==Y
:: case, I don't know why.
@ECHO OFF
SET COMMAND_TO_RUN=%*
SET WIN_SDK_ROOT=C:\Program Files\Microsoft SDKs\Windows
SET WIN_WDK=c:\Program Files (x86)\Windows Kits\10\Include\wdf
:: Extract the major and minor versions, and allow for the minor version to be
:: more than 9. This requires the version number to have two dots in it.
SET MAJOR_PYTHON_VERSION=%PYTHON_VERSION:~0,1%
IF "%PYTHON_VERSION:~3,1%" == "." (
SET MINOR_PYTHON_VERSION=%PYTHON_VERSION:~2,1%
) ELSE (
SET MINOR_PYTHON_VERSION=%PYTHON_VERSION:~2,2%
)
:: Based on the Python version, determine what SDK version to use, and whether
:: to set the SDK for 64-bit.
IF %MAJOR_PYTHON_VERSION% == 2 (
SET WINDOWS_SDK_VERSION="v7.0"
SET SET_SDK_64=Y
) ELSE (
IF %MAJOR_PYTHON_VERSION% == 3 (
SET WINDOWS_SDK_VERSION="v7.1"
IF %MINOR_PYTHON_VERSION% LEQ 4 (
SET SET_SDK_64=Y
) ELSE (
SET SET_SDK_64=N
IF EXIST "%WIN_WDK%" (
:: See: https://connect.microsoft.com/VisualStudio/feedback/details/1610302/
REN "%WIN_WDK%" 0wdf
)
)
) ELSE (
ECHO Unsupported Python version: "%MAJOR_PYTHON_VERSION%"
EXIT 1
)
)
IF %PYTHON_ARCH% == 64 (
IF %SET_SDK_64% == Y (
ECHO Configuring Windows SDK %WINDOWS_SDK_VERSION% for Python %MAJOR_PYTHON_VERSION% on a 64 bit architecture
SET DISTUTILS_USE_SDK=1
SET MSSdk=1
"%WIN_SDK_ROOT%\%WINDOWS_SDK_VERSION%\Setup\WindowsSdkVer.exe" -q -version:%WINDOWS_SDK_VERSION%
"%WIN_SDK_ROOT%\%WINDOWS_SDK_VERSION%\Bin\SetEnv.cmd" /x64 /release
ECHO Executing: %COMMAND_TO_RUN%
call %COMMAND_TO_RUN% || EXIT 1
) ELSE (
ECHO Using default MSVC build environment for 64 bit architecture
ECHO Executing: %COMMAND_TO_RUN%
call %COMMAND_TO_RUN% || EXIT 1
)
) ELSE (
ECHO Using default MSVC build environment for 32 bit architecture
ECHO Executing: %COMMAND_TO_RUN%
call %COMMAND_TO_RUN% || EXIT 1
)
pomegranate-0.13.5/benchmarks/ 0000775 0000000 0000000 00000000000 13740675601 0016230 5 ustar 00root root 0000000 0000000 pomegranate-0.13.5/benchmarks/benchmark_distributions.py 0000664 0000000 0000000 00000011465 13740675601 0023525 0 ustar 00root root 0000000 0000000 # benchmark_distributions.py
# Contact: Jacob Schreiber ( jmschreiber91@gmail.com )
"""
Benchmark the distribution module, printing out the time it takes to do
log probability and training calculations.
"""
from pomegranate import *
import random
import numpy
import time
numpy.random.seed(0)
random.seed(0)
def print_benchmark( distribution, duration ):
"""Formatted print."""
print( "{:25}: {:.4}s".format( distribution.__class__.__name__, duration ) )
def bench_log_probability( distribution, n=10000000, symbol=5 ):
"""Bench a log probability distribution."""
tic = time.time()
for i in range(n):
logp = distribution.log_probability( symbol )
return time.time() - tic
def bench_from_sample( distribution, sample, n=1000 ):
"""Bench the training of a probability distribution."""
tic = time.time()
for i in range(n):
distribution.summarize( sample )
return time.time() - tic
def benchmark_distribution_log_probabilities():
"""Run log probability benchmarks."""
distributions = [ UniformDistribution( 0, 17 ),
NormalDistribution( 7, 1 ),
LogNormalDistribution( 7, 1 ),
ExponentialDistribution( 7 ),
GammaDistribution( 7, 3 ),
GaussianKernelDensity([0, 1, 4, 3, 2, 0.5, 2, 1, 2]),
UniformKernelDensity([0, 1, 4, 3, 2, 0.5, 2, 1, 2]),
TriangleKernelDensity([0, 1, 4, 3, 2, 0.5, 2, 1, 2]),
MixtureDistribution( [UniformDistribution( 5, 2 ),
NormalDistribution( 7, 1 ),
NormalDistribution( 3, 0.5 )] )
]
for distribution in distributions:
print_benchmark( distribution, bench_log_probability( distribution ) )
distribution = DiscreteDistribution({'A': 0.2, 'B': 0.27, 'C': 0.3, 'D': 0.23})
print_benchmark( distribution, bench_log_probability( distribution ) )
distribution = IndependentComponentsDistribution([ NormalDistribution( 5, 1 ),
NormalDistribution( 8, 0.5),
NormalDistribution( 2, 0.1),
NormalDistribution( 13, 0.1),
NormalDistribution( 0.5, 0.01) ])
print_benchmark( distribution, bench_log_probability( distribution, symbol=(5,4,3,2,1) ) )
mu = np.random.randn(4)
cov = np.random.randn(4, 4) / 10
cov = np.abs( cov.dot( cov.T ) ) + np.eye( 4 )
distribution = MultivariateGaussianDistribution( mu, cov )
print_benchmark( distribution, bench_log_probability( distribution, n=100000, symbol=(1,2,3,4) ) )
def benchmark_distribution_train():
"""Run training benchmarks."""
distributions = [ UniformDistribution( 0, 17 ),
NormalDistribution( 7, 1 ),
LogNormalDistribution( 7, 1 ),
ExponentialDistribution( 7 ),
GammaDistribution( 7, 3 ),
GaussianKernelDensity([0, 1, 4, 3, 2, 0.5, 2, 1, 2]),
UniformKernelDensity([0, 1, 4, 3, 2, 0.5, 2, 1, 2]),
TriangleKernelDensity([0, 1, 4, 3, 2, 0.5, 2, 1, 2]),
MixtureDistribution( [UniformDistribution( 5, 2 ),
NormalDistribution( 7, 1 ),
NormalDistribution( 3, 0.5 )] )
]
sample = np.random.randn(10000)
for distribution in distributions:
print_benchmark( distribution, bench_from_sample( distribution, sample ) )
sample = ['A']*2500 + ['B']*3000 + ['C']*3500 + ['D']*1000
distribution = DiscreteDistribution({'A': 0.2, 'B': 0.27, 'C': 0.3, 'D': 0.23})
print_benchmark( distribution, bench_from_sample( distribution, sample ) )
sample = np.random.randn(10000, 5)
distribution = IndependentComponentsDistribution([ NormalDistribution( 5, 1 ),
NormalDistribution( 8, 0.5),
NormalDistribution( 2, 0.1),
NormalDistribution( 13, 0.1),
NormalDistribution( 0.5, 0.01) ])
print_benchmark( distribution, bench_from_sample( distribution, sample ) )
sample = np.random.randn(10000, 4)
mu = np.random.randn(4)
cov = np.random.randn(4, 4) / 10
cov = np.abs( cov.dot( cov.T ) ) + np.eye( 4 )
distribution = MultivariateGaussianDistribution( mu, cov )
print_benchmark( distribution, bench_from_sample( distribution, sample ) )
print( "DISTRIBUTION BENCHMARKS" )
print( "-----------------------" )
print()
print( "LOG PROBABILITY (N=10,000,000 iterations, N=100,000 FOR MVG)" )
benchmark_distribution_log_probabilities()
print()
print( "TRAINING (N=1,000 ITERATIONS, BATCHES=10,000 ITEMS)" )
benchmark_distribution_train()
pomegranate-0.13.5/benchmarks/benchmark_hmm.py 0000664 0000000 0000000 00000013626 13740675601 0021405 0 ustar 00root root 0000000 0000000 # benchmark_hmm.py
# Contact: Jacob Schreiber ( jmschreiber91@gmail.com )
"""
Benchmark the HMM module, including multithreading.
"""
from pomegranate import *
import numpy as np
import time
import random
np.random.seed(0)
random.seed(0)
def global_alignment( match_distributions, insert_distribution ):
"""Create a global alignment HMM from match distributions.
"""
model = HiddenMarkovModel()
i0 = State( insert_distribution, name="i0" )
model.add_state(i0)
model.add_transition( i0, i0, 0.3 )
model.add_transition( model.start, i0, 0.3 )
last_match, last_insert, last_delete = model.start, i0, None
for i, distribution in enumerate( match_distributions ):
match = State( distribution, name="m{}".format(i+1) )
insert = State( insert_distribution, name="i{}".format(i+1) )
delete = State( None, name="d{}".format(i+1) )
model.add_states([match, insert, delete])
model.add_transition( last_match, match, 0.5 )
model.add_transition( last_match, delete, 0.1 )
model.add_transition( last_insert, match, 0.5 )
model.add_transition( last_insert, delete, 0.2 )
if last_delete is not None:
model.add_transition( last_delete, match, 0.7 )
model.add_transition( last_delete, delete, 0.2 )
model.add_transition( insert, insert, 0.3 )
model.add_transition( match, insert, 0.1 )
model.add_transition( delete, insert, 0.1 )
last_match, last_insert, last_delete = match, insert, delete
model.add_transition( last_match, model.end, 0.6 )
model.add_transition( last_insert, model.end, 0.7 )
model.add_transition( last_delete, model.end, 0.9 )
model.bake()
return model
def benchmark_forward( model, sample ):
tic = time.time()
for i in range(25000):
logp = model.forward( sample )[-1, model.end_index]
print("{:16}: time: {:5.5}, logp: {:5.5}".format( "FORWARD", time.time() - tic, logp ))
def benchmark_backward( model, sample ):
tic = time.time()
for i in range(25000):
logp = model.backward( sample )[0, model.start_index]
print("{:16}: time: {:5.5}, logp: {:5.5}".format( "BACKWARD", time.time() - tic, logp ))
def benchmark_forward_backward( model, sample ):
tic = time.time()
for i in range(25000):
model.forward_backward( sample )
print("{:16}: time: {:5.5}".format( "FORWARD-BACKWARD", time.time() - tic ))
def benchmark_viterbi( model, sample ):
tic = time.time()
for i in range(25000):
logp, path = model.viterbi( sample )
print("{:16}: time: {:5.5}, logp: {:5.5}".format( "VITERBI", time.time() - tic, logp ))
def benchmark_training( model, samples, n_jobs ):
tic = time.time()
improvement = model.fit( samples, max_iterations=10, verbose=False, n_jobs=n_jobs , return_history=True)
print("{:16}: time: {:5.5}, improvement: {:5.5} ({} jobs)".format( "BW TRAINING", time.time() - tic, improvement[1].total_improvement[0], n_jobs ))
def main():
n = 15
print("HIDDEN MARKOV MODEL BENCHMARKS")
print("gaussian emissions")
sigma = 3
means = np.random.randn(n)*20
gaussian_dists = [ NormalDistribution(mean, 1) for mean in means ]
gaussian_model = global_alignment( gaussian_dists, NormalDistribution(0, 10) )
gaussian_sample = np.random.randn(n)*sigma + means
gaussian_batch = np.random.randn(50, n)*sigma + means
benchmark_forward( gaussian_model, gaussian_sample )
benchmark_backward( gaussian_model, gaussian_sample )
benchmark_viterbi( gaussian_model, gaussian_sample )
benchmark_forward_backward( gaussian_model, gaussian_sample )
benchmark_training( gaussian_model, gaussian_batch, 1 )
# Reset the model
gaussian_dists = [ NormalDistribution(mean, 1) for mean in means ]
gaussian_model = global_alignment( gaussian_dists, NormalDistribution(0, 10) )
benchmark_training( gaussian_model, gaussian_batch, 4 )
print
print("multivariate gaussian emissions")
m = 10
means = np.random.randn(n, m) * 5 + np.arange(m) * 3
mgd = MultivariateGaussianDistribution
multivariate_gaussian_dists = [ mgd( mean, np.eye(m) ) for mean in means ]
multivariate_gaussian_model = global_alignment( multivariate_gaussian_dists, mgd( np.zeros(m), np.eye(m)*3 ) )
multivariate_gaussian_sample = np.random.randn(n, m)*sigma + means
multivariate_gaussian_batch = np.random.randn(500, n, m)*sigma + means
benchmark_forward( multivariate_gaussian_model, multivariate_gaussian_sample )
benchmark_backward( multivariate_gaussian_model, multivariate_gaussian_sample )
benchmark_viterbi( multivariate_gaussian_model, multivariate_gaussian_sample )
benchmark_forward_backward( multivariate_gaussian_model, multivariate_gaussian_sample )
benchmark_training( multivariate_gaussian_model, multivariate_gaussian_batch, 1 )
# Reset the model
multivariate_gaussian_dists = [ mgd( mean, np.eye(m) ) for mean in means ]
multivariate_gaussian_model = global_alignment( multivariate_gaussian_dists, mgd( np.zeros(m), np.eye(m)*3 ) )
benchmark_training( multivariate_gaussian_model, multivariate_gaussian_batch, 4 )
print
print("discrete distribution")
probs = np.abs( np.random.randn(n, 4) * 20 ).T
probs = (probs / probs.sum(axis=0)).T
discrete_dists = [ DiscreteDistribution({ char: prob for char, prob in zip('ACGT', row)}) for row in probs ]
discrete_model = global_alignment( discrete_dists, DiscreteDistribution({'A': 0.25, 'C': 0.25, 'G': 0.25, 'T': 0.25}))
discrete_sample = list('ACGTAGCTACGACATCAGAC')
discrete_batch = np.array([ np.random.choice(list('ACGT'), size=200, p=row) for row in probs ]).T
benchmark_forward( discrete_model, discrete_sample )
benchmark_backward( discrete_model, discrete_sample )
benchmark_viterbi( discrete_model, discrete_sample )
benchmark_forward_backward( discrete_model, discrete_sample )
benchmark_training( discrete_model, discrete_batch, 1 )
# Reset the model
discrete_dists = [ DiscreteDistribution({ char: prob for char, prob in zip('ACGT', row)}) for row in probs ]
discrete_model = global_alignment( discrete_dists, DiscreteDistribution({'A': 0.25, 'C': 0.25, 'G': 0.25, 'T': 0.25}))
benchmark_training( discrete_model, discrete_batch, 4 )
if __name__ == '__main__':
main()
pomegranate-0.13.5/benchmarks/pomegranate_vs_hmmlearn.ipynb 0000664 0000000 0000000 00000604510 13740675601 0024176 0 ustar 00root root 0000000 0000000 {
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# pomegranate / hmmlearn comparison\n",
"\n",
"hmmlearn is a Python module for hidden markov models with a scikit-learn like API. It was originally present in scikit-learn until its removal due to structural learning not meshing well with the API of many other classical machine learning algorithms. Here is a table highlighting some of the similarities and differences between the two packages.\n",
"\n",
"
\n",
"
\n",
"
Feature
\n",
"
pomegranate
\n",
"
hmmlearn
\n",
"
\n",
"
\n",
"
Graph Structure
\n",
"
\n",
"
\n",
"
\n",
"
\n",
"
Silent States
\n",
"
✓
\n",
"
\n",
"
\n",
"
\n",
"
Optional Explicit End State
\n",
"
✓
\n",
"
\n",
"
\n",
"
\n",
"
Sparse Implementation
\n",
"
✓
\n",
"
\n",
"
\n",
"
\n",
"
Arbitrary Emissions Allowed on States
\n",
"
✓
\n",
"
\n",
"
\n",
"
\n",
"
Discrete/Gaussian/GMM Emissions
\n",
"
✓
\n",
"
✓
\n",
"
\n",
"
\n",
"
Large Library of Other Emissions
\n",
"
✓
\n",
"
\n",
"
\n",
"
\n",
"
Build Model from Matrices
\n",
"
✓
\n",
"
✓
\n",
"
\n",
"
\n",
"
Build Model Node-by-Node
\n",
"
✓
\n",
"
\n",
"
\n",
"
\n",
"
Serialize to JSON
\n",
"
✓
\n",
"
\n",
"
\n",
"
\n",
"
Serialize using Pickle/Joblib
\n",
"
\n",
"
✓
\n",
"
\n",
"
\n",
"
Algorithms
\n",
"
\n",
"
\n",
"
\n",
"
\n",
"
Priors
\n",
"
\n",
"
✓
\n",
"
\n",
"
\n",
"
Sampling
\n",
"
✓
\n",
"
✓
\n",
"
\n",
"
\n",
"
Log Probability Scoring
\n",
"
✓
\n",
"
✓
\n",
"
\n",
"
\n",
"
Forward-Backward Emissions
\n",
"
✓
\n",
"
✓
\n",
"
\n",
"
\n",
"
Forward-Backward Transitions
\n",
"
✓
\n",
"
\n",
"
\n",
"
\n",
"
Viterbi Decoding
\n",
"
✓
\n",
"
✓
\n",
"
\n",
"
\n",
"
MAP Decoding
\n",
"
✓
\n",
"
✓
\n",
"
\n",
"
\n",
"
Baum-Welch Training
\n",
"
✓
\n",
"
✓
\n",
"
\n",
"
\n",
"
Viterbi Training
\n",
"
✓
\n",
"
\n",
"
\n",
"
\n",
"
Labeled Training
\n",
"
✓
\n",
"
\n",
"
\n",
"
\n",
"
Tied Emissions
\n",
"
✓
\n",
"
\n",
"
\n",
"
\n",
"
Tied Transitions
\n",
"
✓
\n",
"
\n",
"
\n",
"
\n",
"
Emission Inertia
\n",
"
✓
\n",
"
\n",
"
\n",
"
\n",
"
Transition Inertia
\n",
"
✓
\n",
"
\n",
"
\n",
"
\n",
"
Emission Freezing
\n",
"
✓
\n",
"
✓
\n",
"
\n",
"
\n",
"
Transition Freezing
\n",
"
✓
\n",
"
✓
\n",
"
\n",
"
\n",
"
Multi-threaded Training
\n",
"
✓
\n",
"
Coming Soon
\n",
"
\n",
"\n",
"
\n",
"
\n",
"\n",
"Just because the two features are implemented doesn't speak to how fast they are. Below we investigate how fast the two packages are in different settings the two have implemented. \n",
"\n",
"## Fully Connected Graphs with Multivariate Gaussian Emissions\n",
"\n",
"Lets look at the sample scoring method, viterbi, and Baum-Welch training for fully connected graphs with multivariate Gaussian emisisons. A fully connected graph is one where all states have connections to all other states. This is a case which pomegranate is expected to do poorly due to its sparse implementation, and hmmlearn should shine due to its vectorized implementations."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Populating the interactive namespace from numpy and matplotlib\n"
]
}
],
"source": [
"%pylab inline\n",
"import hmmlearn, pomegranate, time, seaborn\n",
"from hmmlearn.hmm import *\n",
"from pomegranate import *\n",
"seaborn.set_style('whitegrid')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Both hmmlearn and pomegranate are under active development. Here are the current versions of the two packages."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"hmmlearn version 0.2.0\n",
"pomegranate version 0.4.0\n"
]
}
],
"source": [
"print \"hmmlearn version {}\".format(hmmlearn.__version__)\n",
"print \"pomegranate version {}\".format(pomegranate.__version__)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We first should have a function which will randomly generate transition matrices and emissions for the hidden markov model, and randomly generate sequences which fit the model."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def initialize_components(n_components, n_dims, n_seqs):\n",
" \"\"\"\n",
" Initialize a transition matrix for a model with a fixed number of components,\n",
" for Gaussian emissions with a certain number of dimensions, and a data set\n",
" with a certain number of sequences.\n",
" \"\"\"\n",
" \n",
" transmat = numpy.abs(numpy.random.randn(n_components, n_components))\n",
" transmat = (transmat.T / transmat.sum( axis=1 )).T\n",
"\n",
" start_probs = numpy.abs( numpy.random.randn(n_components) )\n",
" start_probs /= start_probs.sum()\n",
"\n",
" means = numpy.random.randn(n_components, n_dims)\n",
" covars = numpy.ones((n_components, n_dims))\n",
" \n",
" seqs = numpy.zeros((n_seqs, n_components, n_dims))\n",
" for i in range(n_seqs):\n",
" seqs[i] = means + numpy.random.randn(n_components, n_dims)\n",
" \n",
" return transmat, start_probs, means, covars, seqs"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Lets create the model in hmmlearn. It's fairly straight forward, only some attributes need to be overridden with the known structure and emissions."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def hmmlearn_model(transmat, start_probs, means, covars):\n",
" \"\"\"Return a hmmlearn model.\"\"\"\n",
"\n",
" model = GaussianHMM(n_components=transmat.shape[0], covariance_type='diag', n_iter=1, tol=1e-8)\n",
" model.startprob_ = start_probs\n",
" model.transmat_ = transmat\n",
" model.means_ = means\n",
" model._covars_ = covars\n",
" return model"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now lets create the model in pomegranate. Also fairly straightforward. The biggest difference is creating explicit distribution objects rather than passing in vectors, and passing everything into a function instead of overriding attributes. This is done because each state in the graph can be a different distribution and many distributions are supported."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"def pomegranate_model(transmat, start_probs, means, covars):\n",
" \"\"\"Return a pomegranate model.\"\"\"\n",
" \n",
" states = [ MultivariateGaussianDistribution( means[i], numpy.eye(means.shape[1]) ) for i in range(transmat.shape[0]) ]\n",
" model = HiddenMarkovModel.from_matrix(transmat, states, start_probs, merge='None')\n",
" return model"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Lets now compare some algorithm times."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"def evaluate_models(n_dims, n_seqs):\n",
" hllp, plp = [], []\n",
" hlv, pv = [], []\n",
" hlm, pm = [], []\n",
" hls, ps = [], []\n",
" hlt, pt = [], []\n",
"\n",
" for i in range(10, 112, 10):\n",
" transmat, start_probs, means, covars, seqs = initialize_components(i, n_dims, n_seqs)\n",
" model = hmmlearn_model(transmat, start_probs, means, covars)\n",
"\n",
" tic = time.time()\n",
" for seq in seqs:\n",
" model.score(seq)\n",
" hllp.append( time.time() - tic )\n",
"\n",
" tic = time.time()\n",
" for seq in seqs:\n",
" model.predict(seq)\n",
" hlv.append( time.time() - tic )\n",
"\n",
" tic = time.time()\n",
" for seq in seqs:\n",
" model.predict_proba(seq)\n",
" hlm.append( time.time() - tic ) \n",
" \n",
" tic = time.time()\n",
" model.fit(seqs.reshape(n_seqs*i, n_dims), lengths=[i]*n_seqs)\n",
" hlt.append( time.time() - tic )\n",
"\n",
" model = pomegranate_model(transmat, start_probs, means, covars)\n",
"\n",
" tic = time.time()\n",
" for seq in seqs:\n",
" model.log_probability(seq)\n",
" plp.append( time.time() - tic )\n",
"\n",
" tic = time.time()\n",
" for seq in seqs:\n",
" model.predict(seq)\n",
" pv.append( time.time() - tic )\n",
"\n",
" tic = time.time()\n",
" for seq in seqs:\n",
" model.predict_proba(seq)\n",
" pm.append( time.time() - tic ) \n",
" \n",
" tic = time.time()\n",
" model.fit(seqs, max_iterations=1, verbose=False)\n",
" pt.append( time.time() - tic )\n",
"\n",
" plt.figure( figsize=(12, 8))\n",
" plt.xlabel(\"# Components\", fontsize=12 )\n",
" plt.ylabel(\"pomegranate is x times faster\", fontsize=12 )\n",
" plt.plot( numpy.array(hllp) / numpy.array(plp), label=\"Log Probability\")\n",
" plt.plot( numpy.array(hlv) / numpy.array(pv), label=\"Viterbi\")\n",
" plt.plot( numpy.array(hlm) / numpy.array(pm), label=\"Maximum A Posteriori\")\n",
" plt.plot( numpy.array(hlt) / numpy.array(pt), label=\"Training\")\n",
" plt.xticks( xrange(11), xrange(10, 112, 10), fontsize=12 )\n",
" plt.yticks( fontsize=12 )\n",
" plt.legend( fontsize=12 )"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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mkn0xx9bliIiIiIids7tADRAW7EtObh57DqbauhQRERERsXN2GagLjs/TedQi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\n49FHH8X77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"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"evaluate_models(10, 50)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"It looks like in this case pomegranate and hmmlearn are approximately the same for large (>30 components) dense graphs for the forward algorithm (log probability), MAP, and training. However, hmmlearn is significantly faster in terms of calculating the Viterbi path, while pomegranate is faster for smaller (<30 components) graphs."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Sparse Graphs with Multivariate Gaussian Emissions\n",
"\n",
"pomegranate is based off of a sparse implementations and so excels in graphs which are sparse. Lets try a model architecture where each hidden state only has transitions to itself and the next state, but running the same algorithms as last time."
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def initialize_components(n_components, n_dims, n_seqs):\n",
" \"\"\"\n",
" Initialize a transition matrix for a model with a fixed number of components,\n",
" for Gaussian emissions with a certain number of dimensions, and a data set\n",
" with a certain number of sequences.\n",
" \"\"\"\n",
" \n",
" transmat = numpy.zeros((n_components, n_components))\n",
" transmat[-1, -1] = 1\n",
" for i in range(n_components-1):\n",
" transmat[i, i] = 1\n",
" transmat[i, i+1] = 1\n",
" transmat[ transmat < 0 ] = 0\n",
" transmat = (transmat.T / transmat.sum( axis=1 )).T\n",
"\n",
" start_probs = numpy.abs( numpy.random.randn(n_components) )\n",
" start_probs /= start_probs.sum()\n",
"\n",
" means = numpy.random.randn(n_components, n_dims)\n",
" covars = numpy.ones((n_components, n_dims))\n",
" \n",
" seqs = numpy.zeros((n_seqs, n_components, n_dims))\n",
" for i in range(n_seqs):\n",
" seqs[i] = means + numpy.random.randn(n_components, n_dims)\n",
" \n",
" return transmat, start_probs, means, covars, seqs"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false,
"scrolled": false
},
"outputs": [
{
"data": {
"image/png": 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5OEXn4hSdi1PaYpDXJm0kRUVFLF68mLy8PKAheH19PTfccAMrVqygsrKS8vJy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cnlklBc2SiH658K69Biscvbk2JC5RMaz86M5v9HP7NUVODQyqdgraxC3OxfIPPOO3hVSCIaVBi2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\nOs6oBvB0+AV50TMa7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"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"evaluate_models(10, 50)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Sparse Graph with Discrete Emissions\n",
"\n",
"Lets also compare MultinomialHMM to a pomegranate HMM with discrete emisisons for completeness."
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"def initialize_components(n_components, n_seqs):\n",
" \"\"\"\n",
" Initialize a transition matrix for a model with a fixed number of components,\n",
" for Gaussian emissions with a certain number of dimensions, and a data set\n",
" with a certain number of sequences.\n",
" \"\"\"\n",
" \n",
" transmat = numpy.zeros((n_components, n_components))\n",
" transmat[-1, -1] = 1\n",
" for i in range(n_components-1):\n",
" transmat[i, i] = 1\n",
" transmat[i, i+1] = 1\n",
" transmat[ transmat < 0 ] = 0\n",
" transmat = (transmat.T / transmat.sum( axis=1 )).T\n",
" \n",
" start_probs = numpy.abs( numpy.random.randn(n_components) )\n",
" start_probs /= start_probs.sum()\n",
"\n",
" dists = numpy.abs(numpy.random.randn(n_components, 4))\n",
" dists = (dists.T / dists.T.sum(axis=0)).T\n",
" \n",
" seqs = numpy.random.randint(0, 4, (n_seqs, n_components*2, 1))\n",
" return transmat, start_probs, dists, seqs\n",
"\n",
"def hmmlearn_model(transmat, start_probs, dists):\n",
" \"\"\"Return a hmmlearn model.\"\"\"\n",
"\n",
" model = MultinomialHMM(n_components=transmat.shape[0], n_iter=1, tol=1e-8)\n",
" model.startprob_ = start_probs\n",
" model.transmat_ = transmat\n",
" model.emissionprob_ = dists\n",
" return model\n",
"\n",
"def pomegranate_model(transmat, start_probs, dists):\n",
" \"\"\"Return a pomegranate model.\"\"\"\n",
" \n",
" states = [ DiscreteDistribution({ 'A': d[0],\n",
" 'C': d[1],\n",
" 'G': d[2], \n",
" 'T': d[3] }) for d in dists ]\n",
" model = HiddenMarkovModel.from_matrix(transmat, states, start_probs, merge='None')\n",
" return model\n",
"\n",
"def evaluate_models(n_seqs):\n",
" hllp, plp = [], []\n",
" hlv, pv = [], []\n",
" hlm, pm = [], []\n",
" hls, ps = [], []\n",
" hlt, pt = [], []\n",
"\n",
" dna = 'ACGT'\n",
" \n",
" for i in range(10, 112, 10):\n",
" transmat, start_probs, dists, seqs = initialize_components(i, n_seqs)\n",
" model = hmmlearn_model(transmat, start_probs, dists)\n",
"\n",
" tic = time.time()\n",
" for seq in seqs:\n",
" model.score(seq)\n",
" hllp.append( time.time() - tic )\n",
"\n",
" tic = time.time()\n",
" for seq in seqs:\n",
" model.predict(seq)\n",
" hlv.append( time.time() - tic )\n",
"\n",
" tic = time.time()\n",
" for seq in seqs:\n",
" model.predict_proba(seq)\n",
" hlm.append( time.time() - tic ) \n",
" \n",
" tic = time.time()\n",
" model.fit(seqs.reshape(n_seqs*i*2, 1), lengths=[i*2]*n_seqs)\n",
" hlt.append( time.time() - tic )\n",
"\n",
" model = pomegranate_model(transmat, start_probs, dists)\n",
" seqs = [[dna[i] for i in seq] for seq in seqs]\n",
"\n",
" tic = time.time()\n",
" for seq in seqs:\n",
" model.log_probability(seq)\n",
" plp.append( time.time() - tic )\n",
"\n",
" tic = time.time()\n",
" for seq in seqs:\n",
" model.predict(seq)\n",
" pv.append( time.time() - tic )\n",
"\n",
" tic = time.time()\n",
" for seq in seqs:\n",
" model.predict_proba(seq)\n",
" pm.append( time.time() - tic ) \n",
" \n",
" tic = time.time()\n",
" model.fit(seqs, max_iterations=1, verbose=False)\n",
" pt.append( time.time() - tic )\n",
"\n",
" plt.figure( figsize=(12, 8))\n",
" plt.xlabel(\"# Components\", fontsize=12 )\n",
" plt.ylabel(\"pomegranate is x times faster\", fontsize=12 )\n",
" plt.plot( numpy.array(hllp) / numpy.array(plp), label=\"Log Probability\")\n",
" plt.plot( numpy.array(hlv) / numpy.array(pv), label=\"Viterbi\")\n",
" plt.plot( numpy.array(hlm) / numpy.array(pm), label=\"Maximum A Posteriori\")\n",
" plt.plot( numpy.array(hlt) / numpy.array(pt), label=\"Training\")\n",
" plt.xticks( xrange(11), xrange(10, 112, 10), fontsize=12 )\n",
" plt.yticks( fontsize=12 )\n",
" plt.legend( fontsize=12 )"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/home/jmschr/anaconda/lib/python2.7/site-packages/ipykernel/__main__.py:77: DeprecationWarning: converting an array with ndim > 0 to an index will result in an error in the future\n"
]
},
{
"data": {
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AVxJTGTd9G+evXKd3+5o806u+9mYXAoVtERERkRImNj6FcZ9v42JcCo92eogn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\nAIA5qSF4eG0mkmMC3FwZ0fQjiiJOFVRj76dFsNsEzF+WiJV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6ZDBYM1QTEU17Exa2bTYb\nXnjhBbz++us4dOgQwsLCAAAvvPACvvjiC0ilUuTn52Pr1q0TVdKkJZFIsH55MtLjA/H8m6ewbWcx\niqo68dRDOVD7jv0TtyiK6Ow1OVvqDc6vrm3pg8VqdznXVyVHenyQY0714DSQcH/4MVCQBzMZrQNz\nqvsG5lQPjFT3jByqE1O1zrnUIWGO1noM1URENJIJC9tbtmzB7NmzXebkfv755zh16hQ+++wziKKI\nTZs2Ye/evbjlllsmqqxJLTMhGC9vzcOLb+lwqrgFT750EP+2aS7S4oK+9WP2G62ODiDD2urVNPVC\nb3CdV62QSxET5u/SASQuXI1gDedVk+caDNXDu3+0t1wlVGsGQrVzTrUjXHOXRSIiuh4TFrYfe+wx\nZGVl4ZVXXnHetmfPHtx9992Qyx1l3HHHHdi9ezfD9jAaPy88++gCvL+/FG/vKcFP/3gU37ttBm5f\nkviN97Pa7Khv7XOOVA8uXGy7rPuBRAJEBPtiZpIWceGO0erYcH9Ean3Zk5c8Wl+vCbXl/Wivv+js\nV62/aqgOcWmnFxLGUE1ERGNjwsJ2VlbWFbdVVVXhoYcecn4cGxuL9957b6JK8hgyqQQPrkpDRlwQ\nXnhLh1f/cRGFVR1YmiqBIIho6TRc1lqvFw1t/RAum1gdpPZCdmqIc5Q6PkKN6DA/qJScuk9TR2+P\nEccOVOD08RrYbAKAHgCA2hmqhzp/MFQTEdF4c2vKMplMUCqH5jmqVCoYjVf2nSWHrNQQ/H7rMvzX\ndh2OnW/CmUtSvPTJ5zBbXOdV+6jkSIsNdHYAGQzX4zHfm2iy6OkyoODLCpz5qhZ2uwBNoDciExSY\nv2gWQzUREbmNW8O2t7c3LBaL82Oj0QgfH59R76fT6cazrElv/TwVAlX+0JX3I8BHitBIL4QFyBGq\nUSA0QAGNj2xgXrUNQBcs3V0o63Z31eNvun9fDDedroWhz4aKoj7UVRogCoCPnwxJMzSIjveBVCZB\na0cVWjvcXeXkMJ2+L0bDazGE12IIr8WQ6XwtRKsVwqVS2C8UQvnQ/Tf8eG4J24ML7BITE1FTU4MF\nCxYAAGpqapCUlDTq/XNzc8e1Pk8w7ybHDwKvhQOvxZDpci062/tx9IsynNM1QRREBGl9sWRVCmZl\nR0E6sN5gulyLa8FrMYTXYgivxRBeiyHT8VqIgoDeomK0HjiIjoLjsI/hTAu3hG1RdMwlXrNmDf78\n5z/jzjvvhCAIePfdd/H000+7oyQi8hDtLXoc2V+Gi6cbIIqANswPS/JTMGNO1IT3oiciIs9mbGhE\n68FDaDt4CObWNgCAV4gWEbetRUjeMhS3NN/w55iQsN3R0YGNGzcCcIxqb968GTKZDK+//jqWLFmC\nu+66CxKJBLfffjvy8vImoiQi8jCtzXoc2VeKwnONgAiEhvtjyapUZMyOYMgmIqJrZtXr0X60AG0H\nDkF/qRQAIFWpELpyBUKXL4N6RiYk0oGObJ4StoODg7Fr164Rjz311FN46qmnJqIMIvJAzY09OLKv\nDMXnmwAA4ZFqLL0lFWkzwiFhyCYiomsgWK3o0p1G64FD6Dqlg2izAVIpAnKyEbp8GYJungeZl9e4\nfG72fCOiSamxrhtH9pXiUmELACAyJgBLb0lFSkYoN1YiIqJRiaKIvrJytB44iPYjBbDp9QAAn7hY\nhK5YjpClS6AMChz3Ohi2iWhSqa/pwuF9pSgvbgUARMcFYuktqUhKC2HIJiKiUZnb2tB68DDaDhyE\nsaERAKAICEDknbcjdHkefBPiJ7Qehm0imhRqKztweF8ZKksdC1RiE4OwdFUqElK0DNlERPSNbAYD\nOo6dQOuBg+i9WAgAkCqV0C5djNC8ZQiYkwWJTOaW2hi2ichtRFFETUUHDu8rRXW5oxl2fLIWS29J\nQXyS1s3VERHRZCba7eg+dx6tBw6h88RXEAb2blHPnIHQ5csQvGA+5L6+bq6SYZuI3EAURVSVtePw\nvlLUVnYCAJLSQrBkVSpiE4LcXB0REU1m/dU1aD1wEG2HjsDa1QUAUEVGIHR5HkKWLYUqLNTNFbpi\n2CaiCSOKIspLWnF4Xxkaahy/IFMyw7B0VQqiYsd/kQoREXkmS1cX2g4fQduBw+ivqgIAyP38EL5m\nNUKX58EvNWXSTjlk2CaicSeKIkoLW3Dki1I01vUAANJmhmNJfgoiYwLcXB0REU1GdrMZnV+dRNvB\ng+g6cw4QBEjkcgTdPA+hy/MQODcHUoXC3WWOimGbiMaNKIgoudiMI/tK0dzYC0iAzKwILMlPRVik\n2t3lERHRJCMKAnqLi9H65SF0HDsOu8EAAPBLSUHo8mXQLlkEhdqznj8YtolozAmCiOJzjTjyRRla\nm/WQSICZ2VFYnJ+C0HB/d5dHRESTzNC26YdhbnW0fvUK0SJi3RqE5C2DT3SUmyv89hi2iWjMCHYB\nhWcdIbu9tQ8SqQSz50Zj8coUaEP93F0eERFNIte1bboHY9gmohtmtwu4oGvA0f1l6Gzvh1QqwZx5\nMVi8MgVBWve3XSIioslBsFrRdfoM2g4cROfJYdumZ89B6PI8BM0fv23T3YVhm4i+NbtNwLlTdTi6\nvxzdnQZIZRLkLojDohXJCAjycXd5REQ0CUyWbdPdhWGbiK6bzWbH2a/rUPBlOXq6jJDJpbhpUTwW\nLk+GJtDb3eUREdEkMNm2TXcXhm0iumZWqx1nTtSi4EA59D0myOVS3Lw0AQvzkuGvUbm7PCIicjOb\nwYiO48fRduAQei5cBDCwbfqSRQhdnufWbdPdhWGbiEZlMdugO1GD4wcq0Kc3Q6GUYUFeEhYsS4Sf\nmiGbiGg6G9w2ve3gYXQcP+G6bXreUgQvXDAptk13F4ZtIroqs8mGU8eqcfxQBQx9Fii9ZFi0Mhnz\nlybC129qLWAhIqLr42nbprsLwzYRXcFktOJkQRVOHKqE0WCFl0qOpatScfPSBHj7KN1dHhERuYlj\n2/SjaDtwyOO2TXcXhm0icjIaLPj6SBW+OlIFk9EKlbcCebemYd7iBKi8J/+WuERENPbsZjM6vz6F\ntgMH0XXmrMdum+4uDNtEBEO/BScOV+Lk0SqYTTZ4+yiwYm06bloUDy8Vf4ES0dQkCgIEiwWCxQJR\n3wdLdw8kUqljIxWpFBKZ1PXjaTRiOxW3TXcXhm2iaaxfb8bxQxU4WVANq8UOXz8lltyWibkL46D0\n4q8HIppYoihCtFohWCywm82OIGy2DLw1O4Ox3WyBYDEPHRt23D7C+cPPsQ+7j2i1unz+k6MVKL0s\nfF/r+7LBj2XOYxLZdT7GFX8AyEb+g+C6HmPwmGxYjVJYjxyF7n//4tw2XanVImLtrQhZvgw+0dHj\n858/hfHZlGga0veacPxgBU4dq4bNKsBP7YUVa9KRMz8WCiV/LRDREMFmcw2u5mFB+LKgOxh+Rzxu\ndg2+I4ZpqxUQxTH/GqRKpeOflxIylRcUan9IlV6Oj70cx7p6exGoCYAoCIAgQBz4N/x90W4f+Zh9\nhHNtthEf4/L3JytxCm6b7i58ViWaRnq7jTh2oAKnT9TAZhOg1qiwaEUysm+OhVwxvfqeEk1XNoMB\nvUXF6L1YCEthES7+47MrR4GHjQCPRyCUyOWQDoRcqVIJhY8GMi8vl1AsHf6xUjl0fPB+Ix13Puaw\n9xWKawqKOp0O6bm5Y/61fhNRFC8L81cL5lcJ+Ve7j91+TUH/ao/R0NON3Afun3LbprsLwzbRNNDd\nacCxA+U481Ud7HYBmkBvLF6ZgqyboiGXM2QTTWXDw3XPxUL0VVS6BOgeAJBKBwKrI6DK/f2hDFYO\nC79eLsddwq7XZWF4+HGvEcKyUjntNjW5GolEAshkk+56NOt0DNpjiGGbaArr6ujH0f3lOHeyDoIg\nIjDYB0vyUzArNxoyGV8SJJqKbAYj9MXF6LlYiJ4LheirqHCGa4lcDv+0VGhmzoBm1kyU63uRc/PN\nkMjl02rxH9FEYtgmmoI62vpwdH85zuvqIQoigkN8sSQ/BTOzoyBlyCaaUmwGI/QlJei5cPHKcC2T\nDYXrmTPgn54GmWpo11eJTseWbUTjjGGbaIqw2wTUVnfizLEu7NxxAKIIhIT5YUl+KjLnREIq5agV\n0VTgEq4vFqKv/LJwnZriHLm+PFwT0cRj2CbyYL3dRpSXtKKsuBVVZW2wmO0AgLAINZasSkHGrAhI\nGLKJPJrdaERvMcM1kadi2CbyIHa7gLqqTpQVt6KipBWtzXrnscBgH8y5KQxQ9GD12oUM2UQeyhmu\nLxai92Ih9GXlruE6JQWaWTOgnjkD6ox0hmuiSY5hm2iSGxy9Li9pRWVpOyxmGwBALpciKT0Eyemh\nSE4PRXCIHwBH+yoGbSLPYTca0VtyydEt5EIh+srLHf2cMUK4Tk+DzNvbzRUT0fVg2CaaZAZHrwcD\ndmuT6+h11txoJGeEIj4pmBvQEHkgu8mE3uKSEcM1pFL4pyRDPbCgUZ2RznBN5OH4TE00CfT2GFFe\n7AjXVWXtMJsco9cyuRRJaQOj1xlDo9dE5DnsJhP0JZeG5lyXuYZrv+QkaGbNHOgWkg65D8M10VTC\nsE3kBna7gLrqTpQXt6GipBUtTb3OY4HBPpidG42k9FAkJHP0msjTXFO4di5oZLgmmur4LE40QfQ9\npmFzr9tcRq8TU0OQnBGKlIxQBGl9ubkEkQexm83QDyxodIZrm+PnG1Ip/JKSoJnFcE00XTFsE40T\nu11AfXWXM2C3NA6NXgcE+WBWztDca6UXfxSJPIXdbL5y5HqkcD1zBvwz0iH38XFvwUTkVnyGJxpD\nVx29lkmRmKpFckbYQOcQjl4TeQpnuB5sxVdadlm4TnQsZpw5A+rMDIZrInLBsE10AwS7gLoax+h1\nRXErml1Gr705ek3kgexmM/SXStFz4SLDNRHdMD77E10nfa8JFQOj1xWXRhi9Hux7HerH0WsiDzBq\nuE5McLTimzUT6ox0yH193VswEXkUhm2iUQh2AfUDo9fll41eawK9MSsnaqBziJaj10QeQLRa0X3+\ngqPP9cVC6C+VMlwT0bhhMiAaQV+vCeUlbSgvaUFlaTtMRisAx+h1QooWyRmO0WstR6+JPIKtrw8d\nX32N9qPHYD53HoXDWvH5JiQ4FzSqMzIg92O4JqKxw7BNhIHR69rugdHrFjQ3uI5ez5gTieT0UCSk\ncPSayFPY+vvR+fVJtB89hu6z55yj15KwUETMv9kRrjMzGa6JaFwxNdC01ac3o6KkFWXFjs4hg6PX\nUpnEMXo9sGsjR6+JPIfNYETXyVNoLyhAl+6MM2D7JiRAu3ghghctRFFjAxJyc91cKRFNFwzbNG0I\ngoiGmi6UlbSioqQVTfU9zmPDR6/jk7XwUvFHg8hT2E0mdJ7UoWMgYAsWCwDAJy4W2sWLoF20EN5R\nkUN3aGxwU6VENB0xUdCU1qc3o+KSY2FjxSXX0ev4ZMfodUpGKLRhHL0m8iR2sxldp047RrBP6pwB\n2zs6GtoljoDtExPt5iqJiBi2aYoZHL0e3Fhm+Oi1OkCFzKwIpGSEcfSayAPZzWZ0nz6L9oICdJ7U\nQTCZAACqyEhoFy+EdvEi+MbFurlKIiJXTBvk8YwGC+qrDKgu0qGytA1Gw/DR62Akp4chOSMUIRy9\nJvI4gtWKrtNn0VFwDB1ffT0UsMPDnQHbJz6OP9tENGkxbJNHMhosKLnQjKLzjagqbYcgiAC6odao\nkDE/YqBzSAhHr4k8kGC1ovvcebQfPYbOr76G3WAAAHiFhkK79lbHCHZiAgM2EXkEJhHyGEaDBZcu\nNqPw3PCADUREa6AOFrB8VQ5Cwv35BEzkgQSbDT3nL6D96DF0nPgK9v5+AIBXiBZht+RDu3gR/JKT\n+PNNRB6HYZsmNUfAbkHRuUZUlrVBsA8F7MysSGTMjkCQ1hc6nQ6hEWo3V0tE10O029Fz4eJAwD4B\nm74PAKAMDkLoiuUIWbIIfqkpDNhE5NEYtmnScQbs842oLB0K2OFRamRmRSIzKxJBWm5CQeSJRLsd\nPYVFjoB9/ARsvY4NpBSBAYhYtxbaJYvgn5YKiVTq5kqJiMYGwzZNCiaj1TlFhAGbaGoR7Xb0lpSg\n/YgjYFu7uwEACo0G4WtuhXbJQqjT0yGRydxcKRHR2GPYJrcxGa24VNiMorONqBgesCPVyJzDgE3k\nyURBgP5SKdqPFKD92HFYu7oAAHK1GmGrb4F28UJoZmQyYBPRlMewTRPKGbDPNaHiUqtLwM7IikRm\nVgSCQ/zcXCURfRuiKKKvtAztRwvQXnAclo4OAIDc3w9hq/IdAXvWTAZsIppWGLZp3JmMVpQWNqPw\nXBMqL7XBbhcAAGGRg1NEGLCJPJUoiugrr0D70QJ0FByDua0dACDz9UXoyhWOgD17FqRyPt0Q0fTE\n3340LswmKy4VtjimiAwP2BFqZM6JQGZWJAM2kYcSRRH9lVUDI9jHYG5pBQDIfHwQsjwP2sULEZA1\nG1KFws2VEhG5n1vDdkNDA1avXo3Y2FiIogiJRILZs2fjueeec2dZ9C2ZTVaUFrag8NxAwLYNBeyM\nLEfA1oYyYBN5IlEUYaiucQZsU1MzAECqUkG7dAm0ixchMDsLUqXSzZUSEU0ubh/ZDgsLw86dO91d\nBn1LgwG76FwjyocF7NAIf2cXEQZsIs/VX1PrnCJibGgEAEi9vKBdvAjaxYsQkDMHMi8vN1dJRDR5\nuT1sk+cxm2woLXJ0EXEJ2OH+ji4isyOgDfN3c5VE9G0Z6uvRfvQY2o8WwFhXDwCQKpUIXrjAMYI9\nN4cBm4joGrk9bPf19eHxxx9HRUUFoqOj8dOf/hRJSUnuLosuYzbZUFbkmCJSXtLqErAHu4iEMGAT\neSxjQyPaCxwB21BTCwCQKBQImn8ztIsWIuimXMi8vd1cJRGR53Fr2Pb19cXtt9+ORx55BJGRkfjb\n3/6GLVu2YNeuXZBy9zC3GwzYRecbUV7cCttAwA4J93d2EWHApslEtNthbGhAX2U1+quqYCktQ+nh\nAki9lJAqXf/JnLd5Od5efs4I95lq24Ybm5rRUXAM7UePob+qCgAgkcsRNO8mBC9aiKB5cyH38XFz\nlUREnk0iiqLo7iKGmzt3Lt59992rjm7rdLoJrmh6sVkFtDaY0VhrRFuTCYLdcbufRo6IWG9ExKrg\nr2GHAXI/0WKB2NIKobkFYkuL421rG2Czjd8nlcsd/xRySOQKQCF33iZRKEY4phj4WO78WOK8z/Bj\nioHHGHz8gY/HYdBB6O6GUFgMe1ExxIFFjpBKIU1KhCwzA9K0FEhUqjH/vEREnio3N/eG7u/Wke3e\n3l709vYiOjraeZvdbodilHZRN/pFTxU6nW5MroXFPGyKyLARbG2Yn3ORY2j45B7BHqtrMRVMxWth\n6e5Gf2WV419VNfoqq2BuagKGjRVI5HL4xsbANyEBvokJ8E2IR1lbG2bNyITdbIFgGfhnNg97f9jt\nFgvsw49d5RyX2wxG523jMWohkcuvGF3/5lH6wXO8rjin8vx5qKpr0VdW5nhsmQwBOdnQLlqI4Pnz\nIPebPguZp+LPyLfFazGE12IIr8WQsRjkdWvYvnDhAn75y1/igw8+QGBgIN59911ERUUhJibGnWVN\nC4MBu+h8E8qKW2Czel7ApqlHFASYmprRX1WFvoFg3V9VBWtXt8t5Ml9fqGdkwjchAX6J8fBNTIB3\nVNQVfZ0lOh28QkImpG7Bah0WzM1XCfMjBXfzCEHefOW5ZgusPT3Oj/EtXpTsk0qhyZoN7eJFCJ5/\nMxRq/owTEY03t4btRYsWYcOGDXjwwQchk8kQFhaGP/zhD1NuXuRkYTHbUFbciqJzja4BO9RvaA52\nuD+vP00IwWJBf00t+quq0D8wx7q/ugaCyeRynleIFkHzbnKOVvsmJMArNGRSfZ9KpFLIvLwmrEOH\nKIoQbbYrwv1IAX3w/dqmJuTcux4KjWZCaiQiIge3dyN55JFH8Mgjj7i7jCnLYrahvKQVhWddA3Zw\niC8y50RiRlYkAzaNO2uv3hGmB0aq+yurYKhvAARh6CSpFD4x0QPTQByh2jchHgp/jr5eTiKRQKJQ\nDIzk+17TfRp1OgZtIiI3cHvYprE3GLAdI9itsFocqxwHA/bgFBEGbBproijC3NqK/spq9FVWDoTr\nalja213Ok6pU8E9LhW9CPPwSE+CbkACf2BjuPkhERFMOw/YUYbUMThFxzMF2CdiDc7AjGLBp7AhW\nK4z1DS6hur+qCvZ+g8t5isBABOZmuyxcVIWHj0unDSIiosmGYduD2W0Cis83ovCsa8AO0g5NEWHA\nprFg6+9Hf3W1Y271wMJFQ10dxOFt9iQSeEdFwjfHNVgrAwLcVjcREZG7MWx7CEEQ0dnWh6b6HjQ1\n9KCpvgf11Z2w2x19cgcDdmZWBMIi1AzY9K2IoghLR6dzXvXgPGtTc4vLeVKl0iVQ+yUmwCcuFjL2\nZyYiInLBsD0JCXYB7W39aKrvdoTr+h40N/Q4R64BABLATy3HnLnxyMyKRFgkAzZdn8t3WxycCmLr\n7XU5T65WI2BOlrMTiG9iArwjIyCRydxTOBERkQdh2HYzu11Ae0ufa7Bu7HF2DQEAiQQICfNHRLQG\n4dEaREQHIDxSjQsXzyE3N8ON1ZOnsBuNw9rsDUwDqal19GseRhUeDs2MTMeI9eA0kKAg/iFHRET0\nLTFsTyC7TUBrsx5N9d1obuhBY30PWht7nTs2AoBUKkFIuCNYR0RpEBETgLAIfyiU/K+iayP29aHr\n9BlnqO6vqoKx8crdFn1iYwYC9WD/6njIfXzcVjcREdFUxAQ3Tmw2O1qb9C4j1q1Netjtw4K1TIKw\nCLVjxDrKMWIdFuEPuYIvz9M3E0UR1q5uGOrqYKirh3HgraGuHrbeXhQNO/dad1skIiKiscewPQas\nVjtaGnsdU0Dqe9BU343WZj0EYWgkUSaXIizSEawH/4WGqyGTs/0ZXd3ggkVDXR2MdfWOcF3rCNb2\n/n7Xk6VSqMJCIYSHISone9LutkhERDSdMGxfJ4vZ5gzWjq4g3Whr6YM4LFjL5VJExAQgcnDEOkaD\nkDB/yGQM1jQyURBgbmsfFqrrne/bjUbXk6VSeEdGwGf2THjHxMAnJho+MTFQRUZA5uUFnU6H2Nxc\n93whRERE5IJh+xuYTTY0N/a4jFi3t/YNn/oKhVKG6NgARMQEOOZYR2ugDfWDlMGaRiDa7TC1trlM\n+zDW1cFQ3wDBZHI5VyKXwzsyAt4DYdonJho+sTFQRURwCggREZGHYNgeYDJa0TzQv7ppIFh3tPcD\nw4K10kuOmISggWkgAYiI1iA4xA9SKV+iJ1ei3Q5jU/PQ1I+6ehjr6mFsaLiiA4hEoYBPdJRLqPaO\niYYqPBxSOX9EiYiIPNm0fCY3GizO3tWD4bqz3XX+q5dKjvikYIRHaRAZHYCIGA2Cgn0hYbCmYQSr\nFaamZpdpH4a6OhgbGl13V4RjIxhHoHaE6sH3VWFh7FlNREQ0RU35sG3ot7h0BGmq70F3p8HlHJW3\nAgkpWpcR68AgHwZrchIsFhgbG2GorXeZV21qaoJot7ucK1Wp4JuQ4Byh9ol1jFZ7hYRAIuX0IiIi\noulkSoXtfr0ZjQM9rAeDdU+X6+IyH18lktJCEB6tGVjAGICAIG92ayAAgN1shrGhAYbawXZ6jikg\npuYWQBBczpX5+sAvOXkgUA9NAVFqtfx+IiIiIgAeHLb1vSaX+dVN9T3Q97guMPP190JdzqdhAAAc\n6klEQVRyRqhz4WJEtAbqAAZrcuyoaKhvGLZQ0TFabWppddn8BQDkfn5Qp6cN6/wRDe+YGCiDAvm9\nRERERN/II8P27361F316s8tt/moVUjLDXPpY+6tVDEPTnK2/H8b6Bpf+1Ma6Opjb2q84V6HRQD0j\n02WRok9sDBQaDb+PiIiI6FvxyLAtlUmQNiPM0W5vYFtzP7XK3WWRm4iiCNFgQG9RsUvnD0NdHSwd\nnVecrwgMhGb2LEeojh1aqKhQq91QPREREU1lHhm2n/w/q9xdAk0AwWqFtbsbli7HP2t318DbgY+7\numHtcbwvmM24cNn9lVotArLnOKd9DE4Bkfv5ueXrISIiounHI8M2eS7RbodVr3cJzJbubli7ugbe\ndjsDta2v75sfTCqFMiAA3tFRMEqlCJ+ROdD5Iwbe0VGQ+/hMzBdFREREdBUM23TDRFGE3WBwHXUe\nHIV2huluWLq7YO3pvaKrx+Xk/v5QBgXCNzEBysBAKAI0UAQEQBkYMPCx4325v7+zlZ5Op0MCtygn\nIiKiSYZhm65KsFiGAnT3/23v3qOiOO83gD8zswvL/SaiKETURPQkXmLipZh6qScGFEUbq7lp1Hpa\nrelJa6LRatA2tZ5aNYltav2latSktVGPTVMUb0dbI9J6axKjiaAiCIIiF5HFZXfe3x+7O+zCAmpY\nVpjncw5nZt99Z/bdL7vLw8y7u/WOQrsF6/IG34pYn+zvD7+ICJh6dYJfeDiM9YKzfRkBY1gov4qc\niIiI2g2GbZ0RNhtqKytdwnJZvaPPdVM6bLerm9yXpCgwhofbP7EjIhx+4RGOZRiM4RH2EB0RDr/w\ncCgBAa10D4mIiIgeHAzb7YAQArbbtx1vJCxzO+Lsum4pK0dt5V1M4wgNhX+HDjD2rHfUWZvKEQ5j\neAQMwUH8RkQiIiKiJjBsN0EIAWG1QthsEFYbhM0K1bF0bbMvbVCdfZ0/jW1rdb++4XaN7dd92zvl\n5Tjxxw2wlJVDWK1N3hclIADGiHAExHZ2PwrtDNOOqR3GsDDIBj4siIiIiFpCm0xVVz76q3sIbSqc\n2tQGoffutrU1ewTY5xQFIiICQQndGsx9rlu3LxUTP4eciIiIqLW1ybCdv/3j+9pOUhT7j8HgWCqQ\nFANkoxGSyWRvl53tdf1kRz/XbbRtDQogO/u47rvets7r3dYVyPX6Sy63Jde7LdftJEXBqVOnMJCf\nwEFERET0wGqTYfvRt5bfRTitF34VhV+5TUREREStqk2G7bDHHvX1EIiIiIiImsWPkiAiIiIi8hKG\nbSIiIiIiL2HYJiIiIiLyEoZtIiIiIiIvYdgmIiIiIvIShm0iIiIiIi9h2CYiIiIi8hKGbSIiIiIi\nL2HYJiIiIiLyEoZtIiIiIiIvaZNh+3j+KRRUFsGq2nw9FCIiIiKiRhl8PYD7sebY/wEAFFlBbEgM\n4kI7o2tYLOLCOiMuLBadgqIhy23y/wgiIiIiakfaZNh+qd/3kV9RiPzKQhRUXkN+RSGQf1K73igb\nEBvayRHC7QE8LrQzOgZ1YAgnIiIiolbTJsN2auJobV0VKm5Ul6GgohD5FUX2AF5RhILKIuSVF7ht\nZ1SM6BrSSQvgXUM7Iy6sM6KDoiBLDOFERERE1LLaZNh2JUsyOgZFoWNQFB6PfUxrV4WK67dLke8I\n3vkVjhB+6xoulee77cNf8UNX7Sh4Z3QNtU9J6RAYCUmSWvsuEREREVE70ebDdmNkSUZMcDRigqPx\nRJe+Wruqqii5fQP5jgDuDOF5FVeRW5bntg+Twb8uhDsCeNewzogKiGAIJyIiIqJmtduw3RhZltEp\npCM6hXTEk136ae021YbiquuOEF5kn5ZSWYRL5fnIuXnZbR8BRpN9CorrGzNDYxEREMYQTkREREQa\n3YXtxiiygtjQTogN7YTBXQdo7VbVhmtVJSiocBwJryxCQUURLt7Mw4XSS277CDIG2MN3vTdmhplC\nGcKJiIiIdIhhuxkGWbFPJQntjCFxj2vtVpsVRVUljjnhhbjimI5yofQSvr6R67aPYL8gx1xw9zdm\nhplCW/vuEBEREXkkhIBNtaFWtaLWVgtJkiFDgiRJPGj4LTBs3yeDYrAfuQ6LBTBQa6+11aLwVrEW\nwu1TUopw/kYuzl3PcdtHiH9w3VFwbU54LEL9g1v53hAREZEvqUKF1WaFRa1Frc2qBd5aW622brFZ\nYVXtS9f2Wm0bRx9tPy59GtunaoXVsay11dYN6OJmt/FJjtAtS7J9ibp1Z3tjbXeznSTJkKW6pSxJ\nkCA3um3z+2usj/v+3W9TdrufsiQhBmHf+nfLsN3CjIoRD4V3xUPhXd3aLVaLFsKdH0+YX1mEc9dz\n8NX1C259w0yhHkJ4ZwT7BbXmXSEiImpXhBAQEIAAVAhACG15R7Wg8k5V0wHXGWrdAq4VFlstrI5l\nowG3QdC1B2JnMLa10rdiG2UDjIrR/iMbEGg0wc8/BAbFAD/FCKNsxK1btxAaGgJVCKhC1eqmqipU\nCAiXdhUufRztrm1WoWptQqhQhWMJoa27bieEaJU63K2FPX/4rffBsN1K/Ax+6BYRh24RcW7td6wW\nXK28hoLKIsdUFPu88C9LvsaXJV+79Y0whTkCuP0IeJW5HJFl+TAqBvgpfvCT7UujYoBBNvCUDxHp\nhur4I66qNtiECpuwQVVVj+vX79xEXnmB4w+8PURo4UFbr2t3b1Ob384ZTLSQAnugQGPX3127e1td\n0NFCDlwCj6d25zhcri8ru4mDR/8LuN2Gc7wAHLcHCAiBBjWx93UGWGdwBVSogFt/T9u6h96m+8It\nGLuOUevnOm6Xvs4xOfbStIst/tDUSJJk/xstG+x/t2UjTEZ/+MmO4KsY6oJwvUBsVIzwc/xtdwZi\ne3/H0tHPTzFqfQyO23Dtd7fZ4OTJkxg4cGCz/bzFU3hvLOB7Dv1q3T8KLs8Z1zZt3/Wed+7bqUCx\n+q3vD8O2j/kb/NA9Mh7dI+Pd2mtqa1DgCOH5FYWOZRG+KD6PL4rPa/0+uvpPj/uVIGkh3FMY97T0\nkw3wM/g5nrAu7YpR+zE6l7IRfgYj/GT3dob8hoQQsAkVVlstrI65cFbVfrTDarOvu7VrbY52m0v/\nptpt9vbSslIcrP6P+ym0Zk6rNXeqre7Umvuptrrt77FNkrT2xtqketu7nurz2ObhFGa1zYzKmlt1\nvwsPf2wbtHg4qlK/xeMfbdF0n/vZ5u7HV/+2GrppqcDVymuwqTaowhE8m123wabaj0rZHCFWFc7L\njhBb7zpt3XF9Y+ue99NYSG5qPwI2Ybv3o2H5zXfRjdt5zffxwHm6XQIAx+sHHJclSXYs7c9X1zbX\nvval677sfV2fx5Kjjwy5YV/n7aF+X6n5MUlwTFOw35tblbcQHdnBJejWhVTXEFsXcA1uodetj4cg\nrMjKt/9d6YQs2X/XD4KTxSeb79QMhu0HlMloQs+obugZ1c2t3VxbowXv/+V8jojoKO20ldtSrYXF\nWguLWtd+21KtXX9X/+HfB2fId4bv+mG8/rKx6+0/Lv8QyM7g7/kfBVWo9tN49QKoPdDatJDqHmhd\n2t22s8Gq1noItDaXcNywrbaJ9lZXzSShufShr0fw4Lji6wE0TZEVKJIMRVIgy3KDdT+D0bGuQJYk\n936yAlmyr8vN7OfGjRuI6RijzRN1/iNYN1fTHt/q2uQG19fNJW283X0fkvZPZN08Uec/jo5xQGqk\nHXe/nSNgaverfjB1bZNkfP6//6F///4eAqwE12DqKRi3N74+mkvtF8N2GxNgNOHhqAQ8HJWAsDJ/\nDBxw7y8MzncbW2zuYbxuaYHFZnUs6wV4W92Px4Dv4frqWrPW5q2QDwDIbb5LS5MlGQZZgVG2n54z\nOMJ/kNFQ1+44dWeQDY5+itbm3M5+ek+p189Du1JvP479G122+/zzz9G/X/8G8+bcT8epHk+reW5r\neGrN9fSbx1Ny9ba/tzb3y43N6VObanNsf/PmTURGRLr/0jxkBKleo8cYITXfp/5+6m/jabuG29zN\n+Dx2arJPaekNdIyOcQRPl0Aqy5AlpUFg9bQuO/rbw25T64rjNuxtruvuIbnuOlmSG94nLzl58iQG\nPs5QBQABionvByLyMp+H7aysLKxatQrV1dXo0qULVqxYgZiYGF8Pq12TJMke9hQDAhHQarerhXyP\nAd8lpDuOyjcX7l33U1ZRhoiwCEfANXoItIoWVOsHX6Ni9BBoG9+PaxiW5dYLCHfLX/ZDoF/r/V4f\nZDxSVYe1ICLyDZ+GbbPZjPnz52Pjxo1ITEzE1q1bkZ6ejvXr1/tyWOQlbiHf2LJhkEGCiIiIHkQ+\nPSx3/PhxxMfHIzExEQDw/e9/H0ePHkV1dbUvh0VERERE1CJ8GrYvX76MuLi6j8ILDAxEeHg4rlx5\nwN/FQ0RERER0F3wats1mM/z9/d3aTCYTj2wTERERUbvg0znbgYGBuHPnjltbTU0NAgMDm9zu5Mlv\n/5mH7QVrUYe1qMNa1GEt6rAWdViLOqxFHdaiDmvRcnwathMSEpCRkaFdvnXrFiorK9GtW7dGt+Gb\n4IiIiIiorfDpNJIhQ4agsLAQp06dAgBs3rwZI0aMgMlk8uWwiIiIiIhahCTu+TtuW9Z///tfvPXW\nW6ipqUF8fDxWrlyJqKgoXw6JiIiIiKhF+DxsExERERG1Vw/e198REREREbUTDNtERERERF7CsE1E\nRERE5CUPfNi2Wq1YuXIlEhMTUVxcrLX/7ne/wzPPPIOUlBSsWbPGhyNsHQcPHkRaWhrGjh2LF154\nATk5OQD0VwcAyMzMRFpaGlJSUnRfC6fDhw8jMTERhYWFAPRXi6tXr+LRRx9FSkoKkpOTkZKSgjfe\neAOA/moBACUlJZg5cyZGjRqFCRMm4MSJEwD0V4vMzEzt8eB8bPTu3RvV1dW6qwUA7Ny5E2PHjsXY\nsWMxa9Ys5OXlAdDf4wIAdu/ejXHjxmHUqFFYuHAhamtrAeinFvearYqKijBz5kyMGTMGkyZNQnZ2\nti+G7RWN1eLKlSuYNGkSZs6c6db/vmohHnCzZ88W69atE4mJieLatWtCCCE+/fRTMWXKFFFbWyss\nFouYMmWKyMzM9PFIvefatWviySefFLm5uUIIIT788EMxdepU8c9//lNXdRBCiMLCQjF06FBRVFQk\nhBDigw8+EM8++6wua+FkNpvFuHHjxODBg8XVq1d19/wQQoiCggIxatSoBu16rIUQQsyYMUNs3rxZ\nCCFEdna2ePXVV3X9HHHKyMgQr7zyii5rkZubKwYPHixKSkqEEEL85S9/Ec8995wua/HNN9+IwYMH\na5ni5z//ufjDH/6gq1rca7aaNWuW2LJlixBCiHPnzomkpCRx584dn42/JXmqxcWLF0VycrJ48803\nxYwZM9z6308tHvgj2z/5yU8wb948CJcPTcnMzMTEiRNhMBhgNBoxfvx47N2714ej9C6j0Yg1a9ag\ne/fuAOxf7JOTk4O9e/fqqg4AYDAYsHr1anTq1AkAMHToUFy6dEmXtXBat24d0tLSEBQUBEB/z4+m\n6LEW165dw9mzZ/Hiiy8CAAYNGoS1a9fq+jkCABaLBW+//TZef/11XdYiNzcX3bp1Q3R0NAD791xc\nuHBBl7U4fvw4hg4dipiYGADA9OnTsW/fPl3V4l6yVVVVFY4fP47JkycDABITExEbG9tujm57qoXJ\nZMKWLVvQv39/t75VVVXIzs6+51o88GG7X79+DdouXbqE+Ph47XJ8fDwuXrzYmsNqVZGRkRg2bJh2\n+ciRI+jXrx8uX76sqzoAQHR0NIYOHQrAfupn165dGD16tC5rAQBff/01srKy8PLLL2svFHp7fjhV\nVVVh3rx5SE5OxuzZs5Gbm6vLWpw/fx5dunTRTge/9NJLOHfunC5r4erjjz/GwIEDERcXp8ta9OvX\nD/n5+bhw4QKEENi3bx+SkpJ0+dopSRJsNpt2OSgoCHl5ebqqxb1kq7y8PERFRbl94WBcXFy7qY2n\nWnTu3BkdOnRo0J6Xl4fIyMh7rsUDH7Y9qampgZ+fn3bZZDLBbDb7cEStJysrC1u2bMGiRYtgNpt1\nW4ctW7YgKSkJp06dwvz583Vbi2XLlmHp0qVQFAWSJAHQ5/MjKCgIqampWLx4Mfbs2YOkpCTMnTsX\nd+7c0V0tKisr8c0332DQoEHYu3cvxo8fj3nz5umyFk5CCGzatAmzZs0CoM/nSMeOHfHqq68iLS0N\nQ4YMwUcffaTb186hQ4fi2LFjyMnJgc1mw4cffgiLxaLLx4Wrxu6/2WyGv7+/W19/f39d1cbpfmvR\nJsN2QEAALBaLdtlsNiMwMNCHI2odBw4cwOLFi7Fhwwb06NFDt3UAgGnTpiE7OxvTp0/H1KlTIcuy\n7mrx17/+FQ8//DAGDBgAwB4ohBC6fFyEh4djyZIliI2NBQC8/PLLKC0tRVFRke5qERISgujoaIwc\nORIAMHnyZFRUVOiyFk6nT59GUFAQevToAUCff0POnTuH9evX49ChQ8jOzsb8+fMxZ84cXdaiR48e\nWLJkCX72s5/hBz/4AXr27ImQkBBd1sJVY/c/MDAQNTU1bn1ramp0VRunwMBA3Llzx63tbmrRpsK2\n88hd9+7dtXdRA/bD+s4X0fbq2LFjWLFiBTZu3Ig+ffoA0GcdcnNzkZWVpV1OSUlBVVUVunbtqrta\nHDp0CAcPHsSwYcMwbNgwFBcXY/Lkybhx44bualFZWYmCggK3NpvNhhEjRuiuFrGxsbh9+7ZbmyzL\nuqyF0+HDhzF8+HDtsh5fO7OysvD4449r85STk5ORk5ODiIgI3dUCANLS0vCPf/wDO3fuxCOPPIJe\nvXrp8nEBNJ+t4uPjUVZW5nb09vLly+jZs2erj9XX7rcWbSpsO+ekJicn429/+xvMZjNu376N7du3\nY9y4cT4enffU1NRg8eLF+P3vf4+EhAStXW91AICysjIsWLAAJSUlAICTJ0/CZrNh/Pjx2L59u65q\nsWHDBnz22Wc4evQojh49ipiYGOzcuRPp6em6e1x88cUXmD59OsrKygAA27dvR5cuXZCSkqK7x0Wv\nXr3QsWNHfPzxxwCAPXv2ICwsDKmpqbqrhdP58+e1N5gD+nztTEhIwOnTp1FeXg7A/g9IdHQ0nn/+\ned09Lq5cuYK0tDTcunULtbW1WL9+PSZOnIhnnnlGd48LoOlslZqaiuDgYCQlJWHr1q0A7G8wLS0t\nxZNPPunLYbcK5xljp+DgYHznO9+551oYvDrKb6m0tFR7R70kSZg2bRoURcHmzZvx1FNPIS0tDZIk\nITU1FSNGjPDtYL3o4MGDKCsrw2uvvQbA/suXJAnbtm3D2bNndVMHAHjiiScwZ84czJgxA0II+Pn5\nYe3atXjqqadw8eJFXdWiPkmSIITAmDFj8NVXX+mqFklJSXjhhRcwdepUKIqCmJgYrFu3DgkJCTh/\n/ryuagEA77zzDt544w1s2LABUVFRePfdd9G7d2/dvV44FRcXa5/CAUCXz5GRI0fi7NmzmDJlCmRZ\nRnBwMN59910MGDBAd7WIj4/H6NGjMWHCBEiShHHjxiEtLQ0AdFGLe8lWzjNCy5cvx8KFC7Fjxw7t\nsWM0Gn15N1pEY7WYMGECdu/ejaqqKlRVVSElJQV9+/bFypUr76sWknCN7ERERERE1GLa1DQSIiIi\nIqK2hGGbiIiIiMhLGLaJiIiIiLyEYZuIiIiIyEsYtomIiIiIvIRhm4iIiIjISxi2iYiIiIi8hGGb\niKiFpaena1/n+/rrrzfab9OmTUhNTUVycjKefvpp/PKXv0RVVVVrDbNVlJaW4tChQ74eBhGRzzBs\nExG1sNu3byMgIAA2m63RbxZbtWoV9u7di40bN2LPnj345JNPYLFY8OMf/7iVR+tdx48fZ9gmIl17\noL+unYioLXJ+Me/ly5cRHx/f4PqKigps27YNf//737WvETeZTHjzzTdx7NgxAIDFYsGvf/1rZGdn\nQ1EUfPe738WCBQsgSRJGjRqFmTNnYteuXSgpKUF6ejqysrLw73//G5GRkXj//fcREhKCxMRE/OIX\nv8DOnTtx/fp1vPLKK5g6dSoAYMuWLdi+fTuEEEhISMBbb72FiIgILFq0CLGxsTh9+jQuX76MhIQE\nvPfee/D390dubi6WLVuGkpIS+Pv7Y8WKFXj00Ufxn//8B2vWrMGgQYNw4MABWCwWrFy5EoGBgfjV\nr34FVVVhNpvx29/+Funp6Thx4gSEEOjVqxd+85vfICgoqJV+M0RErY9HtomIWsgHH3yAH/7wh/jy\nyy8xb948LFy4EIcPH8ZHH33k1u/MmTPo1KkTunXr5tbu5+eHESNGAAA2b96M4uJi7NmzB7t27cKJ\nEyfw6aefan0vXLiAXbt2Yc6cOViwYAFSUlKwf/9+qKqKffv2af3y8vKwe/dubNu2DStWrEBFRQXO\nnDmDTZs2Ydu2bcjIyEDnzp2xZs0abZvMzEy88847OHDgAEpLS7F//34IITB37lxMnDgRmZmZWL58\nOebOnQtVVQEAX331FQYMGICMjAw899xz+OMf/4g+ffrgxRdfxJgxY7B69WocPXoUV69exd69e5GZ\nmYmePXvizJkzLfxbICJ6sPDINhFRC5k+fTri4uJQU1ODlJQUrFq1CtOmTUNMTIxbv4qKCnTo0KHJ\nfR05cgSzZs2CJEnw9/dHamoqPvvsM6SmpgIARo8eDQB45JFHYDKZ8MQTTwAAevbsiZKSEm0/zz77\nLAAgISEB3bt3x+eff45Tp05hzJgxiIiI0PrMnTtX22b48OEICQnR9l9YWIiLFy+irKwMkyZNAgAM\nGDAAkZGROHXqFAAgODgYI0eOBAD06dMHO3bsaHCfIiIikJOTg/3792PYsGH46U9/ejdlJSJq03hk\nm4ioBX355Zd47LHHAABFRUUNgjZgD53FxcVN7ufmzZsIDQ3VLoeGhqK0tFS77Jx6IcsyAgMDtXZF\nUWCz2bTLYWFh2npISAgqKysb7DssLMxt386g7dyfqqqorKxEdXU1UlJSkJKSguTkZNy8eRPl5eWN\nblNf3759sXTpUmzduhVJSUl47bXX2t0bQomI6mPYJiJqIZMmTcLWrVvxox/9CMnJyThy5AhSUlJw\n/Phxt379+/dHaWkpzp0759ZutVqxdu1a1NTUoEOHDlqQBYDy8vJmj4Z7UlZWpq1XVFQgLCyswb7L\nysoQFRXV5H46duyIkJAQZGRkICMjA3v27MG//vUv7Qj73Xr66aexZcsWHD58GGazGe+///693SEi\nojaGYZuIqIXs2rULI0eOREZGBv70pz9h+vTpyMjIwJAhQ9z6hYSEYNasWViwYAGuXLkCADCbzVi6\ndCnOnz8Pk8mEESNGYMeOHVBVFdXV1fjkk0+0+dz3wjnPOzc3F1euXEG/fv0wfPhw7N+/HxUVFQCA\n7du3a1NAGtOlSxd06tQJmZmZAOxH3ufPn4+ampomtzMYDKisrNTq89577wGwH6nv3r07JEm65/tE\nRNSWcM42EVELycvL0z595MSJExg0aFCjfefNm4fw8HDMmTMHqqpClmV873vfw/LlywEAL730EgoK\nCjB27FjIsozk5GSMGTMGAO4poEZFRSEtLQ0lJSVYsmQJQkJC0LdvX8yePRvPP/88hBDo3bs3li1b\n1uy+Vq9ejfT0dLz99ttQFAUzZsyAyWRqcpukpCRs2rQJkydPxp///GcsWrQIY8aMgcFgwEMPPYSV\nK1fe9X0hImqLJOH8jCoiImpXEhMTceTIEY/zxomIqHVwGgkRERERkZcwbBMRtVOcD01E5HucRkJE\nRERE5CU8sk1ERERE5CUM20REREREXsKwTURERETkJQzbRERERERewrBNREREROQl/w8CuYUPcJ2A\nOAAAAABJRU5ErkJggg==\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"evaluate_models(50)"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.12"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
pomegranate-0.13.5/benchmarks/pomegranate_vs_libpgm.ipynb 0000664 0000000 0000000 00000320435 13740675601 0023646 0 ustar 00root root 0000000 0000000 {
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# pomegranate / libpgm comparison\n",
"\n",
"authors: Jacob Schreiber (jmschreiber91@gmail.com)\n",
"\n",
"libpgm is a python package for creating and using Bayesian networks. I was unable to figure out how to use libpgm to do inference properly without raising errors, but I was able to get structure learning working. libpgm uses constraints for structure learning, a process which is not probabilistic, but can be asymptoptically more efficient (between O(n^2) and O(n^3) as opposed to exponential). To my knowledge, they do not have exact structure learning implemented, likely due to the super-exponential nature of the naive algorithm.\n",
"\n",
"pomegranate has both the exact structure learning problem, and the Chow-Liu tree approximation, implemented. The exact structure learning problem uses an efficient dynamic programming solution to reduce the complexity from super-exponential to exponential in time with the number of variables. The Chow-Liu tree approximation finds the best tree which spans all variables.\n",
"\n",
"Lets compare the structure learning task in pomegranate versus the structure learning task in libpgm for different numbers of variables to compare these speed of the two packages."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Populating the interactive namespace from numpy and matplotlib\n"
]
}
],
"source": [
"%pylab inline\n",
"import seaborn, time\n",
"seaborn.set_style('whitegrid')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Lets first compare the two packages based on number of variables."
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"from pomegranate import BayesianNetwork\n",
"from libpgm.pgmlearner import PGMLearner\n",
"\n",
"libpgm_time = []\n",
"pomegranate_time = []\n",
"pomegranate_cl_time = []\n",
"\n",
"for i in range(2, 15):\n",
" tic = time.time()\n",
" X = numpy.random.randint(2, size=(10000, i))\n",
" model = BayesianNetwork.from_samples(X, algorithm='exact')\n",
" pomegranate_time.append(time.time() - tic)\n",
"\n",
" tic = time.time()\n",
" model = BayesianNetwork.from_samples(X, algorithm='chow-liu')\n",
" pomegranate_cl_time.append(time.time() - tic)\n",
"\n",
" X = [{j : X[i, j] for j in range(X.shape[1])} for i in range(X.shape[0])]\n",
" learner = PGMLearner()\n",
"\n",
" tic = time.time()\n",
" model = learner.discrete_constraint_estimatestruct(X)\n",
" libpgm_time.append(time.time() - tic)"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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FIdDWtlglSyAJ02vnSVPmTExMWLJkCdu3b8fZ2ZlRo0YxePBgevfuXYQRCiGE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\nERERKcCCiYiIiIiISIH/A16W6ZK6bkohAAAAAElFTkSuQmCC\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(14, 6))\n",
"plt.title(\"Bayesian Network Structure Learning Time\", fontsize=16)\n",
"plt.xlabel(\"Number of Variables\", fontsize=14)\n",
"plt.ylabel(\"Time (s)\", fontsize=14)\n",
"plt.plot(range(2, 15), libpgm_time, c='c', label=\"libpgm\")\n",
"plt.plot(range(2, 15), pomegranate_time, c='m', label=\"pomegranate exact\")\n",
"plt.plot(range(2, 15), pomegranate_cl_time, c='r', label=\"pomegranate chow liu\")\n",
"plt.legend(loc=2, fontsize=14)\n",
"plt.xticks(fontsize=14)\n",
"plt.yticks(fontsize=14)\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can see many expected results from this graph. libpgm implements a quadratic time algorithm, and it appears that the growth is roughly quadratic. The exact algorithm in pomegranate is an exponential time algorithm, and so while it does have an efficient implementation that causes the it to be much faster than libpgm's algorithm for small numbers of variables, eventually it will become slower. Lastly, the chow-liu tree algorithm is far faster than both other algorithms because it is finding the best tree approximation. While it is a quadratic time algorithm, it is also a simpler one.\n",
"\n",
"Lets now compare the speed on different numbers of samples."
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"libpgm_time = []\n",
"pomegranate_time = []\n",
"pomegranate_cl_time = []\n",
"\n",
"x = 10, 25, 100, 250, 1000, 2500, 10000, 25000, 100000, 250000, 1000000\n",
"for i in x:\n",
" tic = time.time()\n",
" X = numpy.random.randint(2, size=(i, 10))\n",
" model = BayesianNetwork.from_samples(X, algorithm='exact')\n",
" pomegranate_time.append(time.time() - tic)\n",
"\n",
" tic = time.time()\n",
" model = BayesianNetwork.from_samples(X, algorithm='chow-liu')\n",
" pomegranate_cl_time.append(time.time() - tic)\n",
"\n",
" X = [{j : X[i, j] for j in range(X.shape[1])} for i in range(X.shape[0])]\n",
" learner = PGMLearner()\n",
"\n",
" tic = time.time()\n",
" model = learner.discrete_constraint_estimatestruct(X)\n",
" libpgm_time.append(time.time() - tic)"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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5coRff/2VVq1aERUVxZUrV2jfvr26fsuWLXTq1IlatWqxePFiGjRogJOTExqN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"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(14, 6))\n",
"plt.title(\"Bayesian Network Structure Learning Time\", fontsize=16)\n",
"plt.xlabel(\"Number of Samples\", fontsize=14)\n",
"plt.ylabel(\"Time (s)\", fontsize=14)\n",
"plt.plot(x, libpgm_time, c='c', label=\"libpgm\")\n",
"plt.plot(x, pomegranate_time, c='m', label=\"pomegranate exact\")\n",
"plt.plot(x, pomegranate_cl_time, c='r', label=\"pomegranate chow liu\")\n",
"plt.legend(loc=2, fontsize=14)\n",
"plt.xticks(fontsize=14)\n",
"plt.yticks(fontsize=14)\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"It looks like when fitting for the same number of variables that pomegranate is able to scale much better than libpgm is. This could mean that for large datasets, pomegranate is much faster than libpgm even though it has a worse theoretical notation.\n",
"\n",
"However, it's also important to note that this isn't exactly a fair comparison because they are two different algorithms. libpgm is implementing the constraint based structure learning algorithm which is quadratic in time, and pomegranate is using an exact structure learning algorithm which is exponential in time. However, this benchmark should lay out some practical speed differences when deciding which package to use."
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.12"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
pomegranate-0.13.5/benchmarks/pomegranate_vs_sklearn_gmm.ipynb 0000664 0000000 0000000 00002151224 13740675601 0024673 0 ustar 00root root 0000000 0000000 {
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# pomegranate / sklearn GMM comparison\n",
"\n",
"authors: \n",
"Nicholas Farn (nicholasfarn@gmail.com) \n",
"Jacob Schreiber (jmschreiber91@gmail.com)\n",
"\n",
"sklearn is a very popular machine learning package for Python which implements a wide variety of classical machine learning algorithms. In this notebook we benchmark the GMM implementations in pomegranate and compare it to the implementation in sklearn. In sklearn, GMM refers exclusively to Gaussian mixture models, while in pomegranate it refers to General mixture models, as it is flexible enough to allow any combination of distributions or models to be used as components.\n",
"\n",
"However, a simpler version of the GMM is kmeans clustering. Both pomegranate and sklearn implement these, so lets take a look at those first."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Populating the interactive namespace from numpy and matplotlib\n"
]
}
],
"source": [
"%pylab inline\n",
"import seaborn, time\n",
"seaborn.set_style('whitegrid')\n",
"\n",
"from sklearn.mixture import GMM\n",
"from sklearn.cluster import KMeans\n",
"from pomegranate import *"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Lets create some functions to evaluate models efficiently. We can start with fitting and predicting against an increasing data size. The data we compare against are Gaussian blobs which are 3 standard deviations away from each other to allow for some, but not a lot of, overlap."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"def create_dataset(n_samples, n_dim, n_classes):\n",
" \"\"\"Create a random dataset with n_samples in each class.\"\"\"\n",
" \n",
" X = numpy.concatenate([numpy.random.randn(n_samples, n_dim) + i*3 for i in range(n_classes)])\n",
" y = numpy.concatenate([numpy.zeros(n_samples) + i for i in range(n_classes)])\n",
" return X, y\n",
"\n",
"def plot( fit, predict, skl_error, pom_error, sizes, xlabel ):\n",
" \"\"\"Plot the results.\"\"\"\n",
" \n",
" idx = numpy.arange(fit.shape[1])\n",
" \n",
" plt.figure( figsize=(14, 4))\n",
" plt.plot( fit.mean(axis=0), c='c', label=\"Fitting\")\n",
" plt.plot( predict.mean(axis=0), c='m', label=\"Prediction\")\n",
" plt.plot( [0, fit.shape[1]], [1, 1], c='k', label=\"Baseline\" )\n",
" \n",
" plt.fill_between( idx, fit.min(axis=0), fit.max(axis=0), color='c', alpha=0.3 )\n",
" plt.fill_between( idx, predict.min(axis=0), predict.max(axis=0), color='m', alpha=0.3 )\n",
" \n",
" plt.xticks(idx, sizes, rotation=65, fontsize=14)\n",
" plt.xlabel('{}'.format(xlabel), fontsize=14)\n",
" plt.ylabel('pomegranate is x times faster', fontsize=14)\n",
" plt.legend(fontsize=12, loc=4)\n",
" plt.show()\n",
" \n",
" \n",
" plt.figure( figsize=(14, 4))\n",
" plt.plot( 1 - skl_error.mean(axis=0), alpha=0.5, c='c', label=\"sklearn accuracy\" )\n",
" plt.plot( 1 - pom_error.mean(axis=0), alpha=0.5, c='m', label=\"pomegranate accuracy\" )\n",
" \n",
" plt.fill_between( idx, 1-skl_error.min(axis=0), 1-skl_error.max(axis=0), color='c', alpha=0.3 )\n",
" plt.fill_between( idx, 1-pom_error.min(axis=0), 1-pom_error.max(axis=0), color='m', alpha=0.3 )\n",
" \n",
" plt.xticks( idx, sizes, rotation=65, fontsize=14)\n",
" plt.xlabel( '{}'.format(xlabel), fontsize=14)\n",
" plt.ylabel('Accuracy', fontsize=14)\n",
" plt.legend(fontsize=14) \n",
" plt.show()\n",
" \n",
"def evaluate_kmeans():\n",
" sizes = numpy.around( numpy.exp( numpy.arange(8, 16) ) ).astype('int')\n",
" n, m = sizes.shape[0], 20\n",
" \n",
" skl_predict, pom_predict = numpy.zeros((m, n)), numpy.zeros((m, n))\n",
" skl_fit, pom_fit = numpy.zeros((m, n)), numpy.zeros((m, n))\n",
" skl_error, pom_error = numpy.zeros((m, n)), numpy.zeros((m, n))\n",
"\n",
" for i in range(m):\n",
" for j, size in enumerate(sizes):\n",
" X, y = create_dataset( size, 1, 2 )\n",
"\n",
" pom = Kmeans(2)\n",
" skl = KMeans(2, max_iter=1, n_init=1, precompute_distances=True, init=X[:2].copy())\n",
"\n",
" # bench fit times\n",
" tic = time.time()\n",
" skl.fit( X )\n",
" skl_fit[i, j] = time.time() - tic\n",
"\n",
" tic = time.time()\n",
" pom.fit( X, max_iterations=1 )\n",
" pom_fit[i, j] = time.time() - tic\n",
"\n",
" # bench predict times\n",
" tic = time.time()\n",
" skl_predictions = skl.predict( X )\n",
" skl_predict[i, j] = time.time() - tic\n",
"\n",
" tic = time.time()\n",
" pom_predictions = pom.predict( X )\n",
" pom_predict[i, j] = time.time() - tic\n",
"\n",
" # check number wrong\n",
" skl_e = (y != skl_predictions).mean()\n",
" pom_e = (y != pom_predictions).mean()\n",
"\n",
" skl_error[i, j] = min(skl_e, 1-skl_e)\n",
" pom_error[i, j] = min(pom_e, 1-pom_e)\n",
" \n",
" fit = skl_fit / pom_fit\n",
" predict = skl_predict / pom_predict\n",
" \n",
" plot(fit, predict, skl_error, pom_error, sizes, \"samples per component\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Below we see the fit and predict speeds for the two algorithms on increasing dataset sizes. pomegranate is always faster than sklearn for both prediction and fitting steps. These numbers fluctuate a bit every run and so running it multiple times (20 in this case) and reporting mean and standard deviations is ideal. Since these are unsupervised algorithms, accuracy is kind of a weird metric, but it refers to assigning cluster labels correctly corresponding to the underlying distribution which generated the data."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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pFB+tri53KUIMsN1xeC+bpTWfJ+372L2Bp4RBPWIYuFqzMZPhnXSa6ZEIe1dU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EpLSzl16hRw9+/X1tYWgDp16gB3ezLXrl1LdnY2b775ps7irK3mzp3L2bNnee2114C7ic+1a9fQ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\n8P84yik1BmDBRAAAAABJRU5ErkJggg==\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
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vLaGAJCIiIiJ9xtwFz9O0vp54Yj2z5z3JniPHEAyEOGDU12hcV8Nrbz2N49is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\nu+94+eWXJTlyMH9/f+Lj4+nevTs7d+5k7dq1pKen88ADDxAVFWVfGJ0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"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"evaluate_kmeans()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The lines show the mean of the plotted value, and the bounds show the minimum and maximum value. We can see that kmeans looks liks it's between 5-10x faster per fitting iteration than sklearn is, and around 3-4x faster when it comes to prediction! To confirm that the two are getting the same results, we plot the unsupervised 'accuracy' for the two, and see that they are identical. \n",
"\n",
"Lets now look at Gaussian datasets with two components when running Gaussian Mixture Models. We'll look at how many times faster pomegranate is, which means that values > 1 show pomegranate is faster and < 1 show pomegranate is slower. Lets also look at the accuracy of both algorithms. Accuracy should be roughly the same, but different, since both have different random initialization points. The measured the time is the time it takes to do a single iteration of EM."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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PGiGEEEJMjwnDz2te8xpe85rXAPCnf/qn/OAHP5jyk+VyOdasWcOHP/xhzjzzTNatW0cQ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\n796sWrWKj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"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
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FpIhrdLtO1UJ7PyPbFboeicN/u2TDjsgOOd1f2LGlRCJbtbEQM1OIJaw+VZzE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"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"def evaluate_models():\n",
" sizes = numpy.around( numpy.exp( numpy.arange(8, 16) ) ).astype('int')\n",
" n, m = sizes.shape[0], 20\n",
" \n",
" skl_predict, pom_predict = numpy.zeros((m, n)), numpy.zeros((m, n))\n",
" skl_fit, pom_fit = numpy.zeros((m, n)), numpy.zeros((m, n))\n",
" skl_error, pom_error = numpy.zeros((m, n)), numpy.zeros((m, n))\n",
"\n",
" for i in range(m):\n",
" for j, size in enumerate(sizes):\n",
" X, y = create_dataset( size, 1, 2 )\n",
"\n",
" pom = GeneralMixtureModel( NormalDistribution, n_components=2 )\n",
" skl = GMM( n_components=3, n_iter=1 )\n",
" \n",
" # bench fit times\n",
" tic = time.time()\n",
" skl.fit( X )\n",
" skl_fit[i, j] = time.time() - tic\n",
"\n",
" tic = time.time()\n",
" pom.fit( X, max_iterations=1 )\n",
" pom_fit[i, j] = time.time() - tic\n",
"\n",
" # bench predict times\n",
" tic = time.time()\n",
" skl_predictions = skl.predict( X )\n",
" skl_predict[i, j] = time.time() - tic\n",
"\n",
" tic = time.time()\n",
" pom_predictions = pom.predict( X )\n",
" pom_predict[i, j] = time.time() - tic\n",
"\n",
" # check number wrong\n",
" skl_e = (y != skl_predictions).mean()\n",
" pom_e = (y != pom_predictions).mean()\n",
"\n",
" skl_error[i, j] = min(skl_e, 1-skl_e)\n",
" pom_error[i, j] = min(pom_e, 1-pom_e)\n",
" \n",
" fit = skl_fit / pom_fit\n",
" predict = skl_predict / pom_predict\n",
" plot(fit, predict, skl_error, pom_error, sizes, \"samples per component\")\n",
"\n",
"evaluate_models()"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": true
},
"source": [
"Lets also see how well it scales as we add more components where there are 10,000 total data points. "
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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kjz1tJcNzFWF0zPexhZiWCnIzjYMg92KOlw8GJBMmSxybZc7sVv2qIuxRPZVe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\n7ty/n9ZIhHVhCfHTk8npD8UTArU8Bq0W1pYCeLrmBsMKTbf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N+11kV+hdyk5hcq0O7mjv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\n2sj8Q0MAAAAASUVORK5CYII=\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
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CZ6wgJjfXiAlYY6iJoyGWerD5XCzWrA7YX1k2l68r5rLee4oxpaX5DuXbG1Cx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\nRv45CCGE/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"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"def evaluate_models():\n",
" sizes = numpy.arange(2, 21, dtype='int')\n",
" n, m = sizes.shape[0], 20\n",
" \n",
" skl_predict, pom_predict = numpy.zeros((m, n)), numpy.zeros((m, n))\n",
" skl_fit, pom_fit = numpy.zeros((m, n)), numpy.zeros((m, n))\n",
" skl_error, pom_error = numpy.zeros((m, n)), numpy.zeros((m, n))\n",
"\n",
" for i in range(m):\n",
" for j, size in enumerate(sizes): \n",
" X, y = create_dataset(10000 / size, 1, size )\n",
"\n",
" pom = GeneralMixtureModel( NormalDistribution, n_components=size )\n",
" skl = GMM( n_components=size, n_iter=1 )\n",
" \n",
" # bench fit times\n",
" tic = time.time()\n",
" skl.fit( X )\n",
" skl_fit[i, j] = time.time() - tic\n",
"\n",
" tic = time.time()\n",
" pom.fit( X, max_iterations=1 )\n",
" pom_fit[i, j] = time.time() - tic\n",
"\n",
" # bench predict times\n",
" tic = time.time()\n",
" skl_predictions = skl.predict( X )\n",
" skl_predict[i, j] = time.time() - tic\n",
"\n",
" tic = time.time()\n",
" pom_predictions = pom.predict( X )\n",
" pom_predict[i, j] = time.time() - tic\n",
"\n",
" # check number wrong\n",
" skl_e = (y != skl_predictions).mean()\n",
" pom_e = (y != pom_predictions).mean()\n",
"\n",
" skl_error[i, j] = min(skl_e, 1-skl_e)\n",
" pom_error[i, j] = min(pom_e, 1-pom_e)\n",
" \n",
" fit = skl_fit / pom_fit\n",
" predict = skl_predict / pom_predict\n",
" plot(fit, predict, skl_error, pom_error, sizes, \"number of components\")\n",
"\n",
"evaluate_models()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Looks like pomegranate can be much faster than sklearn at this task--around 10x faster for the fitting step. The reason that the accuracies vary is because a different random initialization is used for each model.\n",
"\n",
"Now lets take a look at Multivariate Gaussian models. For sklearn the initialization is exactly the same, but for pomegranate the MultivariateGaussianDistribution object must be passed in instead of the NormalDistribution object."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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MM+WrTvomy2Dey0Kmb6yrKYadd5JJnqirY20yGfqiuyIiIiLSd4QKPyeccALz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tzIrVu3tP2DBg1i79692vbGjRuJiIgwRIiiijMxdABCCCEEgK+vr7ZGh7W1NR4eHnTo0AEfHx9S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\n2p45cybz5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"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
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LZK8Msygx1aCm/BP9kHUevoioc4QjIBsy/BP9yJ2VC2Ow0eXxPlqeBm9fb4wjJEpN8ZgV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"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"def evaluate_models():\n",
" sizes = numpy.around( numpy.exp( numpy.arange(8, 16) ) ).astype('int')\n",
" n, m = sizes.shape[0], 20\n",
" \n",
" skl_predict, pom_predict = numpy.zeros((m, n)), numpy.zeros((m, n))\n",
" skl_fit, pom_fit = numpy.zeros((m, n)), numpy.zeros((m, n))\n",
" skl_error, pom_error = numpy.zeros((m, n)), numpy.zeros((m, n))\n",
" \n",
" for i in range(m):\n",
" for j, size in enumerate(sizes):\n",
" X, y = create_dataset( size, 5, 2 )\n",
" \n",
" pom = GeneralMixtureModel(MultivariateGaussianDistribution, n_components=2)\n",
" skl = GMM( n_components=2, n_iter=1 )\n",
" \n",
" # bench fit times\n",
" tic = time.time()\n",
" skl.fit( X )\n",
" skl_fit[i, j] = time.time() - tic\n",
"\n",
" tic = time.time()\n",
" pom.fit( X, max_iterations=1 )\n",
" pom_fit[i, j] = time.time() - tic\n",
"\n",
" # bench predict times\n",
" tic = time.time()\n",
" skl_predictions = skl.predict( X )\n",
" skl_predict[i, j] = time.time() - tic\n",
"\n",
" tic = time.time()\n",
" pom_predictions = pom.predict( X )\n",
" pom_predict[i, j] = time.time() - tic\n",
" \n",
" # check number wrong\n",
" skl_e = (y != skl_predictions).mean()\n",
" pom_e = (y != pom_predictions).mean()\n",
"\n",
" skl_error[i, j] = min(skl_e, 1-skl_e)\n",
" pom_error[i, j] = min(pom_e, 1-pom_e)\n",
" \n",
" fit = skl_fit / pom_fit\n",
" predict = skl_predict / pom_predict\n",
" plot(fit, predict, skl_error, pom_error, sizes, \"samples per component\")\n",
"\n",
"evaluate_models()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Looks like pomegranate is faster in the fitting step for multivariate Gaussian mixture models and roughly the same speed for making predictions. The accuracy seems to be pretty much overlapping for these at near perfect.\n",
"\n",
"Lets see how the two models scale when changing the dimensionality of the data between 2 and 20 dimensions."
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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//jgPP/ww55xzDh6Ph3vuuYfZs2cXO9/wYYBqy6PlkthHVXSfDSQGVKPHwxWN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lAAAg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\n8yGTyTBu3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"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
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7nCQJVL+nGlo9fV6Je+hEaXBQgkTKRmsI1oFLa9Qgs5QgkeBSNAUiQmdIibti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\nR6d8jgsvvBCrVq1Ce3s7GGO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YhBBCzuSHdkAheBWH3ujvk+oFtXi/9KUvIZlM4sknn8Rb\nb70FRVHQ2tqKz372s/jkJz9Z6hhJDmNONZDhN4Zdn/RG6x+VHuMMPMrLPtdsJiIuoKjeTgLKQcQE\neJRDGt6eixSk8e2EEBI0fmgHzEba0reV68YrqNWrKAo+/elP49Of/nSJwyGzCZ8TxvDrw4CLo2Ro\n/pF7lGoFdo93vxhp/tH01HoV2WPZcocxI+oFJoQQb+NxDrvbu+2AWUkgfLa/h9cBBc5B6u3tpTLf\nHsE1Dq3Z3UUeZVZCb/X/2QA/8HKFMduwoTXSAqPT0Vt0T48dtzO0/QghxOu83A4ohN6sQxH+H2lS\n0Du4++67qcy3h4TPcbdYA49wiCp/77B+oaU0z3atM8Z8P6a4lLSU5umDAuMMIkH7MSGEeJnaoMLO\neLMdMBs7awei9wgocIjdSy+9RGW+PUSr0SASAvaQOzsQrX/kHrXWu0MZ1aRKE/xnwBiDmlJhdBvl\nDmVKolr4dsE+QgipFGqNWmD3hfeIpICa8G47Zi6ozLdPhZeGXVmcUkpJCZKLmMI8O0+E5h/NTmvU\nylJlshC8mgo0EEKI13m5HTATaUmElwSj9wigMt++FVoSwtCBIaDEbTGZlQi1UllnN/E4h93lre51\nO2PTOlgFCLWGMPCbATDurZ4aKSUlSIQQ4hM8zmGPeKsdMBvGGUJnBae9OO8y34sXL8Ztt92GK664\nouAX27ZtG1555RUwxrBlyxasXr0aAHDixAls3rw5f78jR47gy1/+MgzDwPe+9z0sXrwYALB+/Xrc\nfvvtc3l/gcUYg96qY+TwSEmHzfAqDh6mhpWbRLWA0eWtYVpKSAlMt3kpMc6g1Wkw+721ErrMSuhN\nlOASQogfiGoB44S32gGz0Vv0QA3Dn1eZ72w2i+effx4/+9nP8K1vfQsHDhyY9Tn27NmDw4cPY/v2\n7ejs7MSWLVuwfft2AEBDQwMefvhhAIBpmvjkJz+Jyy+/HDt37sS1116LO+64Y55vL9giKyIY7hwG\nU0v3gaThde5TG1QM/W4Iiuad4as0vK5wakqFccrw1HwfJhh4jE50EEKIH2iNGob2D3l+8fFRdtZG\nZEWk3GEU1ZxaPX/84x/x+OOP46mnnoJlWbjmmmvw6KOPFvTY3bt3Y9OmTQCAtrY29Pf3Y3BwENFo\ndML9nnzySVx99dWoqqqaS2gViYc4tAYNZl9pzlZLW3q6aEBQqQlvTdCUtoRWR+WhCxVaGsLQ/iEw\n3TsJEhVoIIQQ/xBx4bmh2jPRUhp4JFgn4ZiUcsZZLENDQ/jFL36Bxx9/HL///e9x6aWX4qWXXsLP\nf/5zLFu2rOAXuvPOO7Fx48Z8knTTTTdh69atWLp06YT73XDDDfjhD3+IaDSKHTt24JFHHkEikYBp\nmrjjjjsmlBqfSkdHR8ExBYHdZ8P6rQUmir8jyawEfy/3zRmMIDFfMoFMuaNw0Odg7sw9JjBS7ijG\nqQfEudQLSAghfuG548g0pCnB38Wh1PuzjbB27dopr5/xiPn1r38dzz77LJYsWYIPfehDeOCBB1BX\nV4c1a9ZAVRfWszBVXrZ3714sW7Ys36t0wQUXIJlM4rLLLsPevXtxxx134Omnn571uad7s27r6Ohw\nJZY+9M1rMl/nwU60LW+b9namMtSur11IaPPm1t9uvkodX7/dD+Od+Y0/nm27zpWiK0iuTxbt+by8\nbYsV26A2iJE3i39km8+2lVKi6rwqRJaXdvhDJWzXUvFyfF6ODfB2fF6ODfB2fF6ODXAnvtPyNLLH\ns3N+XLHbALNhKkPt+wtvK3pp287UqTJjgvTkk0/immuuwRe+8AUsX758QUGkUin09PTkL3d1daG+\nvn7CfV588UWsW7cuf7mtrQ1tbc5GXrNmDfr6+mBZFjgPVjfeQuln6Uj/Ll307liad1I+IibmnSAV\nG81Dm7vQWSGk/5D2RK+bzEhojTREkhBC/ETEBTLHMp4eHi3t4FY6nvHo/fDDD0NVVXzsYx/DRz7y\nEfz4xz9GT0/PvDbWhg0bsHPnTgDAgQMHkEqlzph/tG/fPqxcuTJ/+cEHH8QzzzwDAHj99deRTCYp\nOZpCZHmk6HNWaP5ReWmNmidW0pamhNZAjeu5EtUCvMob31VMYxBRSnIJIcRPtEYNMuPNdfXybASu\nOMOoGY+aF198MS6++GLceeed+PnPf46f/exn+Pa3vw0pJXbt2oU/+7M/K3io3YUXXohVq1ahvb0d\njDHcdddd2LFjB2KxGK688koAQHd3N2prx7rpPvjBD+IrX/kKHnvsMZimia1bty7grQYXUxj0Rfq8\numKnIw2JUEswzwr4gVcmaEopoTdTeej5UFMqsseKt0/Ol4hTckQIIX4jYgJMK387YCbaIg2KKP9I\niVIo6MgZi8Vw88034+abb8a+ffvw+OOP47777sN3v/tdXH/99fj6179e0IuNX+sIwITeIgBnzC9q\nbKiQhZUAACAASURBVGzMl/8mM4ucG8HImyNFG9IjYsJTZaYrDWMMolrASltljUNNqoFa18BNeovu\n7JNl3o9ogVhCCPEnERewBsrbDpiOnbURXh4udxglM+dTi+9617vwrne9C1//+tfxi1/8Ak888UQp\n4iJzJKoE1JQKq784OxLNOyk/Xs3LnyDRMMt501IaFLW8yZG0JUQN7cuEEOJHvJp7NkESCQGtNrhD\n8Od99A6Hw/jYxz6Gxx57rJjxkAUIt4VhGwuftyItCbWeGsblJhJiymqPbrEzNrTm4H75lRpjDGqq\nvPuRNGgOGSGE+JWoEZC29+YhSUsitCTY0zBoDFWAhJpDRVmoS5o078QLtEYNMlu+L0ZFU6DWUKK8\nEFqjBmmVcRvqCkSEepAIIcSP9EYd0vBegsQUhvDS4A6vAyhBCpzQ4tCCzzaIuCj70CAC8CgvyQLA\nhRJ1wtPlRf0g1BoCynhsE9WUHBFCiF/xsDcXaddb9MDPT/beX50sSPic8MITJJqz4AmMsbJVIJNS\nQk1S79FCMc7KOo+LCjQQQoi/ee1El52xEV4R7N4jgBKkwFGEsqDy3DT/yFvK1cCVWYnQWcEeX+wW\ntV4ty1wyaVGBBkII8Tse99aJLjWlQlQF/9hCCVIAhc8Jw87Or1gDzT/yFhEvT6EGHuXgYW99KftV\naGmoLHPJpCGhN9G+TAghfiZqRFnnso5nGzbCy4LfewRQghRIalyd97AekRCBXfTLj7Sm8hRqoPLe\nxcNDvCzFLpSw4smx64QQQgqnN+mQpjcSJB7iFXMSnY6eARVeGp7XDkXrH3mLqHJ/wV5pybKXpw4a\nUe/+fuW1ceuEEELmTtEUKOHyN9ellNAX6xVTvKn8f3FSEvpifc5nj6UpodXTmile43qhBhsLmsdG\nzhQ+a/7DXufLa+PWCSGEzI8nTnhZzhSOSkEJUkAxxqC36nObvyIBfVFldJ36iRJzdzcVCQHGK+MM\nkVtEXBRljbJCSYuqEBJCSFB44YSX1qiBa+WPwy2UIAVYeEUYMAu/v4hTw9iL3F5JW9R64ExVALlZ\nHVKaEloD9QYTQkgQqLVqWechyaxEeHnl9B4BlCAFGtc4tKbCG0k0/8ib9EbdtUINdtamXsQS0Zt1\n2IY7w+x4hLs+d40QQkhpaA1aWSvZ8WpecVMw6AgacOFzwpDG7DuVbdhQG2hIjhfxMIcScmdXZYJB\nraPPQSlojZprFSJpgVhCCAkORSjgVWVaF9GS0M+qvBOnlCAFnFarFdxY0hsrbwfwC7cmaKq1asVU\nqHEbY8y1anaUIBFCSLCUbR4SAyLLI+V57TKiBKkChJaGZu2aVWtUMIUaxl7lxhejlJLWPyoxvVEv\n+TAJadJ2JISQoClXJTu9Wa/I9qGrf+1t27bhlVdeAWMMW7ZswerVqwEAJ06cwObNm/P3O3LkCL78\n5S/j/e9/P772ta/h2LFj4JzjW9/6FlpbW90MORDCS8NIH0jPeB+af+RtokZg5M2RkhbRkFlnjQNS\nOqHFIQzuHQRKmO9KS0JLVdZYcUIICTq1TkX69TQU1b2+DTtrI7Ki8nqPABd7kPbs2YPDhw9j+/bt\n2Lp1K7Zu3Zq/raGhAQ8//DAefvhh/OhHP0JTUxMuv/xyPPPMM6iursajjz6Kz3/+87j//vvdCjdQ\nmOKU/J6ObdhU8crj9Ea9oLlkC8GrOEQVJcqlxDgree8Or+KuHkAJIYSUnlavgUl3e3LUOhUiVpnt\nAteOort378amTZsAAG1tbejv78fg4OAZ93vyySdx9dVXo6qqCrt378aVV14JAFi/fj1+85vfuBVu\n4ERWRKZdqJIxRmecPU7RFSiR0u6uVN7bHWpKndv6ZHNE848IISR4GGfgURfX0zMlwksqq7T3eEyW\n8kg9zp133omNGzfmk6SbbroJW7duxdKlSyfc74YbbsAPf/hDRKNR3HrrrfjqV7+KlStXAgA2btyI\n//zP/4SmTd+Y7+joKN2b8DnztyZweoobIoC4iBrHXmfuNYGB0jy3tCX4ORzKIup5KDU7Y8P6fxaY\nWqIzgYsAsZz2Z0IICRpznwmcdOnFFIBv4IEv3LR27dopry/bUXSqvGzv3r1YtmwZotFowY+ZynRv\n1m0dHR2eiQUAMs0ZnN51Ot8w6zzYibblbdDP0hFbHStzdBN57W83WTniG1AHkDmcmfV+o9t1Luys\njbpr6lwpQ+3lbetWbH3pPtjDc18TabZtaxs24uvjZalISdt1/rwcn5djA7wdn5djA7wdn5djA8oX\n31B4CMOdwzPeZz5tgMmkdHqPoqunbo8vhJe27UydKq6dLk6lUujp6clf7urqQn19/YT7vPjii1i3\nbt2Ex3R3dwMADMOAlHLG3iMyM71RP6OOvp21oTfRxHw/UGvUklVAUxOqa2v0EGeYXUnYqLjF/Agh\npFKoDSrsTOkXHJemRHhF5Q6vA1xMkDZs2ICdO3cCAA4cOIBUKnVGT9G+ffvyw+lGH/Pss88CAF54\n4QW8+93vdivcwNLP0iHtsUY247QwqF9ojRqkWZoEieYfuSu0OFSSgxyP8pJWOiSEEFI+ao3qSstd\na9DA9cqez+paq+jCCy/EqlWr0N7eDsYY7rrrLuzYsQOxWCxfiKG7uxu1tbX5x1x77bXYtWsXPv7x\nj0PTNNx7771uhRtYkbMjSL82VvJbraGFQf1CURXwCC96L5KdtaE1Ua+Dm9SECl7Fi57wlm0hQUII\nISXHFAYRE7BHSteLJA1ZkQvDTubqaePxax0BmNBbBABPP/30hMujax+R4mGcQW/RkT2eBUDrH/kN\nr+YwT5pFfU7GqYphOaj1an4/LJZyLSRICCHEHTzOS5og8SpOS7/AxSF2xDtGS35LQ0JbRDuBn4h4\n8RvAapJ6EctBb9ZhG8U7yNlZmxJdQggJuFKeCJO2/P/bu+/4Gs//j+OvM3KyCEHMGLGjRCJISKzQ\nUFVRtWeHBuXXVquKUlWiStEvpdGpqFGzKWrVJmaNhFKrESPRGIlE5CQ51++PyKk0ie2ck/o8H48+\nKvd9n/u8z32fcV/3tbCvKP3SQQpITyV9YT12bnagy7o4FgWHvpj+sTfLkv5H1mEobXis/YU0mic/\nCa0QQgjrMpQxPLmBGlRWVwwhBaSnlqOHIzgjNQcFjKGU4bH2QTKlmXCo4PDY9ifun0ajybpR8Zjo\nCunQaOXzLIQQ/2V6Fz0a/ZP5rrcvZy8D/dwmBaSnlL27PbrK0qG7oNHqtbmGan8UOicd+sJSg2Qt\nhtKPr8ArAzQIIcR/n0ajeSK/2yajCacaUnuUTQpITymNRoO2uJz+guhxXghL8zrrcqjgAI+ppYQU\ndIUQ4unwJG6I6YvpZaCfO8gVshAFzOP6AlMm9VibeIkHp9VrH0u/IVOaCbtSci6FEOJpoC+qR6nH\n19xeZSgcKz3dE8P+mxSQhChg7ErYPZbRz1SGwqG89D+yNjs3u0f/odPdnkBQCCHEf56hlAGV9vgK\nSBo7DQ6V5HrgTlJAKuBq1KjB5s2b81wXFBTE/PnzLZxIPGkGNwMa9eidKPUuerR28hVgbQ4eDo/8\nQ6cvpJcBGoQQ4imhL6xHY3h83/n27vYyaNe/yNWREAWMRqdBV+jR2x9L/yPboHPUoS/6aOdCBmgQ\nQoiny+OaF1EGZ8ibFJCEKIC0Lo/20TWlm7AvI5PB2Qq7ko/WPE461gohxNNF5/J4bowZShnQOcpN\ntn+TAlIB8PXXXxMUFETdunVp2bIl8+bNy3O75ORkXnjhBT799NNc60wmE1988QXPPvssdevWpUOH\nDkRHR5vXx8bG0r9/f/z8/GjQoAEDBw7k8uXL5vU1atTg+++/p0mTJsyYMYM9e/ZQr149duzYQZs2\nbfDx8SE0NJTk5OQ8s6WlpfHhhx8SGBiIj48PnTp14uDBg+b1qampfPjhh/j5+eHn50d4eDg3b97M\nc93w4cPN6/7djHDPnj3UqFGDlJSUPHMDrF69mhdeeAEfHx+aNWtGeHh4jqwRERG0adMGb29vOnfu\nzOHDh7l48SI1a9bk6NGjObZt374933zzTZ6v+Ul61AtijUaDoZThMaURj8q+gj3K+HDN7ExpJgyl\n5VwKIcTTRO+qR5kerXm2Kd2EQxXpe5SXp/q24/qrVzl2+0L6SYg1GtkeG5tjWS1nZ4KLFbvvffz+\n++/MmDGDJUuWUKNGDY4cOUK/fv1o2LAhNWrUMG9nMpkYOnQoHh4eDBs2LNd+5s6dy88//8zs2bMp\nX748y5cvJywsjJCQEIoWLcqoUaNwc3Nj+/btpKWl8cYbb/Dpp58yZcoU8z7WrVvH8uXLKVGiBHv3\n7iU1NZVffvmFn376iRs3btCxY0eWL19Onz59cj3/N998w759+4iIiMDFxYVp06bx1ltvsW3bNgCm\nTp3KiRMnWLNmDVqtll69evHZZ5/x4Ycf5lo3YMAA87r7cWfu8+fP89577zFr1iyaN2/OkSNH6NGj\nB3Xq1CEgIIDo6GhGjx5NeHg4DRo04LvvvqN///5s2bIFPz8/IiIieOaZZwCIiYnh5MmTvPDCC/d9\nPh8XQ0kDN4/fRGt4uHscdsXspM+KDTG4GtA6ah9qTiSNTvPYmloIIYQoGOxL25O8PxmNw8P/luud\n9TiUkQJSXqQGycbduHEDACenrPahXl5e7N69O0fhCGDSpEkkJiYyefLkPDvaLVmyhL59+1K5cmXs\n7Ozo2rUrJUuWZO3atQDMnj2b8ePHYzAYKFy4MEFBQTlqmACee+453NzczPs3mUy88soruLi4UK5c\nOby8vDh9+nSer6N///4sWbKEYsWKodfradu2LfHx8Vy+fBmlFCtXruTll1+mePHiuLq6EhoaSqtW\nrfJcN378eFq1anXfx/DO3O7u7kRGRtK8eXPz8fTw8DC/1pUrV+Ln50ejRo3Q6/W8/PLLjBo1ivT0\ndF588UVWr15NZmYmkFXwatiwIaVKlbrvLI/Low4NLf2PbM/DDrmud9FL51ohhHjK6Bx1aB0e/jJe\nmRT25aWpfX6e6quk4GLFHqg250EduHwZ3/LlH2kfjRo1onHjxjz33HM0bNiQwMBAXnzxRVxdXc3b\nLFu2jA0bNhAREYG9fd5v9nPnzjFx4sQcze8yMzO5dOkSANHR0UybNo3jx49jNBoxmUy5LvzLlSuX\na7/u7u7mfzs6OpKWlpbn81+5coWwsDD27t2boxme0Wjk2rVrJCUl5diXu7s7vr6+XL16Nde6atWq\nUa1atTyfJy//zr1w4UKWLVtGfHw8SinS09MxGo1AVlPDO5/LYDDQrl07AIKDgxk7diyRkZE4Ojqy\nfv16evTocd85HieNNmsmbVPagw/3bUozyfDeNshQzsCt2FsPPLLg42qHLoQQomDRu+jJSMp4uAcr\ncKwucx/lR2qQbJzBYCA8PJylS5fi6+vL8uXLadu2LbF3NN07duwY/v7+fPbZZ/nux8HBgUmTJhEV\nFWX+b968eQwZMoTExERCQ0OpXbs2mzdvJioqKs9mejpd7gux+71zPWTIEK5du8by5cuJjo5m6dKl\n5nVabdbbMK+5YO62Li8mU+4Cw525lyxZwuzZsxkzZgy///47UVFR1KxZM8fryWsfkFWL17p1a1at\nWkVCQgKnTp0iODj4vnI9CQ87cpnWQStNsmyQfRn7B272qJR65BHwhBBCFEyPMoKpoawBrV6KAfmx\n6JGZMGECXbt2pVu3bhw5ciTHukuXLtG9e3c6depk7luyZ88e/P396d27N71792bcuHGWjGsTMjIy\nSEpKombNmgwaNIiVK1dSuHBhNmzYYN5m5MiRTJkyhaioKBYuXJjnfipUqMCJEydyLPv7778BOHPm\nDCkpKbz22mu4uLgA5BqM4FEdOXKErl27UrZsWYAczfeKFi2Ki4sLZ86cMS87d+4cS5YsyXPdiRMn\nWLJkCZBVgExNTc3xuLuJioqiXr16BAYGotfrSU5OJiYmxry+fPnynD171vy3yWTi+++/Jz4+HoAO\nHTqwadMmdu3aRYsWLShUqNDDHI7H4mEHapDmdbZJo9E88Gh2yqhkgAYhhHhK6V31D9V31ZRmwrGa\n1B7djcUKSHv37iUmJobFixcTFhZGWFhYjvUTJ07k1VdfZenSpeh0Oi5evAhAw4YNmTdvHvPmzWP0\n6NGWimszvv32W3r37s358+cBOHv2LNevX6dChQrmbXQ6HSVKlGDs2LFMmjQpxwV/tu7du7Nw4UL2\n799PZmYmv/32G8OGDePMmTOULVsWrVbLwYMHSU1NZfHixZw9e5bExERu3br1WF5H+fLlOXz4MOnp\n6URGRrJ+/XoAc8GjY8eOfPvtt8TFxZGYmMjcuXPNhah/rxs/frx5XaVKldi6dSupqanExsaycuXK\nu+Zwd3fn7NmzXLt2jbi4OEaPHk2ZMmVy5Dhw4AAbN24kPT2d+fPnM3v2bHNByM/Pj0KFChEREUH7\n9u0fy7F5WHal7DAZH6yJnTIpDCXkgtpWGUobHujHTqN/PHNiCSGEKHjsy9ijMh68gKR31WNwlWuB\nu7FYASkyMtLcsb5KlSokJiaa+6KYTCYOHDhAUFAQAGPGjDHXNDztXnnlFerVq0eXLl2oW7cuAwcO\npF+/fnkOUtC6dWtatmzJsGHDzAMJZHvppZfo06cPQ4YMoV69ekyfPp3BgwdTuXJlSpUqxbBhwxgz\nZgzNmjXj9OnTTJ8+naJFiz62JmQffvghmzdvpmHDhnz//fdMmDCBwMBA+vXrx/Hjx3n33XepX78+\n7dq1o3Xr1ri5ufHee+8B5Frn7u5uXvf222+TlJSEv78/77zzDv369btrju7du1OlShWCgoLo27cv\nISEh9OvXj1WrVjFt2jQ8PT35/PPPmThxIg0aNGDVqlXMnj0bZ2dnIOsuf/v27dHpdDRp0uSxHJuH\nZVfU7oE/wSpdOmXaMocKDpB57+2y6YvIAA1CCPG00hq0aB0f7EJAZSocKkk/5HvRqPvt3PGIRo8e\nTbNmzcwX9j169CAsLAwPDw8SEhLo2bMnTZo04ejRo9SvX593332XPXv2MHbsWCpUqEBiYiKDBw8m\nICDgrs9z4MABS7wc8RT76quvcHZ2pmfPntaOQsaeDMh7XIy8GUDvL03sbFnGgQy439kH3EDvKedT\nCCGeVhkHM+DG/W+vlELfRC9Tfdzm6+ub53Kr/bLeWS5TShEfH0+fPn0oV64coaGhbNmyBU9PTwYP\nHsxzzz1HbGwsffr0Yf369RgMd68WzO/FWtqBAwdsJktebDmfrWbbsmULv//+O2FhYTaRL9GUSHpc\neo5lp0+dpkrVKnlubyhrwMXXxRLR8mWr5xZsI1uKYwo3T93Ms2boznOrlMK5ljNOVZ0sHTFPtnDs\n8mPL2cC289lyNrDtfLacDWw7ny1nA9vKd8PuBmkx/9wpvds1AIB9OXsK1ytsiWh5sqVjd7dKFYsV\nkEqWLElCQoL578uXL+Pm5gaAq6srZcuWNferadSoESdPnqR58+a0bdsWyBpkoESJEsTHx1P+EYfO\nFuJhtGnTBqPRyKRJk8yDWVibvrA+VwEpPypDYSglbY5tnYOHAylHU+45+Z8yKgxl5HwKIcTTzK64\nHbdO30Kjv3eNkMlowqmmbdxUs3UW64MUEBDAunXrgKwR0kqWLGnu+K7X6ylfvjx//fWXeb2HhwcR\nERF8++23QNaIa1euXLHKpJxCAKxdu5ZNmzbRokULa0cxM5Q23PdcSEop7MtK/yNbp3PU3dfQ3VqD\nFr2zNK8TQoinmaHU/Q/uY+dmh85JBva5Hxb7da1Xrx7PPPMM3bp1Q6PRMGbMGJYvX07hwoV59tln\nGTlyJMOHD0cpRfXq1QkKCuLmzZsMHTqU3377jfT0dD766KN7Nq8T4mmiL6JHo7u/dsR2xeykzXEB\nYVfSjrRzd+9cJhPECiGE0Oq16Jx19xzNzpRholAV601NUtBY9Pbj0KFDc/x95wSdFStWzDWHT6FC\nhQgPD7dINiEKIo1Gg95FT+bNew99Zlf8webYEdZjX96eW6duoTHkX6CVApIQQgjImjA240rG3bdx\n0OFQTkavu18yha4QBdz9XCib0kwYyknta0FhKGa469CtyqTQu0rzOiGEEPeeOF4pmeLjQUkBSYgC\nTl9Uz71G69faazEUkwJSQaJ3y/8HT6Ur7EvLj50QQoisvkWm9Lv0R84Ax+qOlgv0HyAFJCEKOENp\nAyrt7gUkfXGpbSho7Mva5/uDp7XXonOUJnZCCCHAUMKARuXfJNtQ1oDOIL8ZD0IKSEIUcLpCOjR2\n+X8xKqWk/1EBZF/GPt8BOO7VnEIIIcTTQ6PToCuUdwFIpSscq0nt0YOSApIQBZxGo0Ff5C7NsdIU\nDhWkY2ZBo9FqsCuRd8FWV0TuBAohhPhHfr8LOhcdhuLSxP5BSQFJFGh//PEHO3bssHYMq7vbQA26\nwjppjlVAGUobUKaczSdVprqveZKEEEI8PfJqWaAyFQ6V5Abpw5ACkijQli5dys6dO60dw+r0RfS5\nLqSzSfO6gsuhogP8awR3la6wLyMDNAghhPiHXSm73BPHa8GxsjSvexhSQLJx58+fp0aNGqxbt452\n7dpRp04dunXrRnx8vHmbgwcP0q1bN+rVq0fjxo0ZP348RqMRgOXLl/P888+zZMkSAgMDqV+/Pt99\n9x27du3i3XffxcfHh9GjR5v3lZaWxvjx42nRogXe3t50796dP/74w7z+yJEjtG7dmrp16/L666+z\naNEi/Pz8cmT98ccf8fPzY/ny5QDMnTuX4OBgfHx8ePbZZ1m6dKl5fzNmzGDAgAF88803BAQE0KBB\nAz799FPz+mvXrjFkyBAaN26Mr68vffr04fTp0wCMGTOGH3/8kR9++IGgoCAAEhMTee+99wgMDMTH\nx4fXX3+d8+fP53t8V69ezQsvvICPjw/NmjXLNe9WREQEbdq0wdvbm86dO3P48OF7rpsxYwYdO3bM\nsZ+goCDmz58PwPDhwxkxYgR9+/YlODgYgNjYWPr374+fnx8NGjRg4MCBXL582fz42NhY+vXrZ875\n1VdfAfDyyy8zfvx4DGUMqPSsAtLaw2vpObknkHX3yK6kFJAKKq1ei841Z+2f1kmL1l6+uoUQQvzD\nztUu11W9fTl7mSD+IT3V7TSurr9KyrGUJ7Z/Y6yR2O2xOZY513KmWHCxB97XvHnz+Prrr3F2dubt\nt99m5MiRfPvtt1y9epVXXnmFt99+m7lz53Lu3DlCQ0MpXLgwb731FgAXL17k/PnzbNq0iXnz5jFt\n2jRatWrFuHHjsLOzo2/fvnTt2pXatWvz2WefERUVxcKFC3F1deXLL79k4MCBbNiwAaUUAwYMoG3b\ntgwdOpR9+/YxYsSIXFkjIyPZuHEjhQoVYv/+/Xz66acsWbIET09PNm/ezKBBg6hXrx6VK1cG4NCh\nQ3h5ebF582Z27dpF//79qV69Or6+vkyePJmEhAQ2bNiAXq9n5MiRfPDBByxatIixY8dy5swZateu\nzfvvvw/AiBEjUErxyy+/YGdnR1hYGO+++y6LFy/OlfP8+fO89957zJo1i+bNm3PkyBF69OhBnTp1\nCAgIIDo6mtGjRxMeHk6DBg347rvv6N+/P1u2bOHMmTOMHz8+z3X3Y9OmTYSFhdGyZUsARo0ahZub\nG9u3byctLY033niDTz/9lClTpgAwePBg6tevz4wZMzh//jw9e/akQoUKdOjQgUmTJjF8+HC0hqxv\nxn1n99G6XuusJzKBg7tUrxdkhpIGUm+kotFk/cjJAA1CCCH+TaPVoC/8z++DKc2EUw0nKyYq2OQ2\nZAHRrVs3ypQpg4uLC6+++iqRkZGkpqbyyy+/ULJkSV5++WUMBgNVq1ale/furFmzxvzY1NRUQkND\nMRgMNG/eHKPRSIcOHXBycsLf3x8nJydiYmIwmUwsW7aMAQMGULp0aezt7XnzzTdJSUlh9+7dREVF\nceXKFd544w0cHBxo0qQJTZo0yZW1Q4cOFC5cGI1Gg6+vL5GRkdSqVQuNRkNQUBCOjo4cO3bMvL1S\niv79+5vzOTg4cOHCBQA++ugjZs+ejbOzM/b29rRu3Zro6Og8j9GVK1f47bffGDJkCK6urhQqVIhh\nw4Zx+PBhzpw5k2t7d3d3IiMjad68OQBeXl54eHiY979y5Ur8/Pxo1KgRer2el19+mVGjRpGens72\n7dvzXXc/ypQpQ6tWrcwXvbNnz86qCTIYKFy4MEFBQeYcx44d4/jx4wwaNAhHR0eqVavG9OnTqVSp\nEsHBwaSmprJz5070RfQkJCVwOv40wfWyaqb0rvp8R0ITBYNDJQeU8Z/mk/czMbAQQoinz50DNdi5\n2aEvJDfUHtZTfeSKBRd7qNqc+3X5wGXK+5Z/LPvy8PAw/7ts2bJkZmaSkJBAbGysuSYmW8WKFc0F\nDAAXFxecnZ0BsLfP6rtQqlQpUlKyas8MBgNpaWlcuXKFlJQU/u///s984Q5gMpmIi4ujcOHCODk5\nUazYP8esTp06bNq0KcfzlytXzvzvjIwMZs2axdq1a7ly5QoARqPR3AQw+/XodP98qB0cHMzrY2Ji\nmDhxIlFRUdy8eRMg30JIbGxWbd1LL72UY7lOp+PSpUu5jhPAwoULWbZsGfHx8SilSE9PNz93bGws\n7u7u5m0NBgPt2rUD4PLly9SqVSvPdfejbNmyOf6Ojo5m2rRpHD9+HKPRiMlkolSpUgCcO3cu13H3\n9/c3/7tNmzZERETg09OHbVHbqF66OqVdSwMy/9F/gd5Zj76wHpPRlNVkspg0mRRCCJFbdgsDU7qJ\nQpULWTlNwSZXTwVEZuY/PbWVyrqbrNFochQ07nRnAefOf2fTanNXHjo4ZDXF+vHHH6lbt26u9WvW\nrEGvz/mWyWs/dxZ2Zs6cyapVq5g1axa1a9dGq9XSoEGDfLPeyWQy0b9/f7y9vVmzZg0lSpRgWupc\nUQAAIABJREFU48aNDBo0KM/ts/Nv3ryZEiVK5LnNnZYsWcLs2bOZMWMG/v7+6PV6OnTokCOXyZT3\nRJ13W5eXO88fkOM4JiYmEhoaSufOnfnyyy9xcXHhhx9+4IcffgCyjvHdnqtDhw7079+fkf1GsiVq\nC42rNwbAZDRJZ/7/CLuSdqSdT4PMrJHthBBCiH8zlDGgjAqdvQ57d/n9fxTSxK6AyK4dgaw+RXq9\nHjc3NypUqMDZs2dzbHvmzBkqVqz4wM9RuHBhXF1dOXHiRI7l2YMcFC9enBs3bnDjxg3zuiNHjtx1\nn1FRUQQFBeHl5YVWqyU2NpakpKT7ypOQkMCFCxfo3bu3ucBz9OjRfLd3d3dHp9PlyG8ymbh48WK+\n2erVq0dgYCB6vZ7k5GRiYmLM68uXL5/j2JpMJr7//nvi4+MpWbJkvuvs7e25deuWeV1qaioJCQn5\n5j5z5gwpKSm89tpruLi45Hqd5cuX59atW1y6dMm8bOvWrebhzRs2bEixYsVYu3ctx84do2HlhgBo\n9PnPoyMKFvuK9iijQuOgQWsnX9tCCCFy07voQQf25e3zvfks7o/80hYQixYt4vLlyyQmJjJnzhwC\nAwOxt7enbdu2XLp0iblz55Kens7x48dZsGABL7744kM9T/fu3QkPD+fPP/8kIyODxYsXExISQlJS\nErVr18bJyYnw8HCMRiM7d+4kMjLyrvtzd3fn+PHj3Lx5k7NnzzJx4kRKlSqVYxS+/BQrVgwnJycO\nHTqE0Whk3bp17Nu3D8D8eHt7e86fP09SUhLOzs60a9eOKVOmcOHCBdLS0pgxYwa9e/fOVYOTne3s\n2bNcu3aNuLg4Ro8eTZkyZcz77tixIwcOHGDjxo2kp6czf/58Zs+eTaFChWjatGm+6ypWrEhMTAx/\n/PEHaWlpfP755zg55d9RsmzZsmi1Wg4ePEhqaiqLFy/m7NmzJCYmcuvWLTw9PalVqxbTpk0jOTmZ\n06dPM3LkSHNBU6PREBISwrQZ0/Cr4YeTfdZz2RW3ky/I/whDMQMaBw04WzuJEEIIW6XRaNDYa3Cs\nIUN7PyopIBUQISEhvPrqqwQGBpKSksK4ceOArIvrmTNnEhERgZ+fH2+++Sa9evXilVdeeajnGThw\nIEFBQfTp04cGDRqwYsUKvvrqK3M/pv/973+sXr0aPz8/lixZwquvvppnM7tsAwYMQKvV0rhxY4YM\nGUJoaChdu3blyy+/ZNGiRXfNotfrGTduHN999x3+/v5s2LCB6dOnU6tWLZ5//nmuXbtGx44d2blz\nJ88++yzp6emMGjWKKlWqEBISQkBAAIcOHWL27Nk5mv1l6969O1WqVCEoKIi+ffsSEhJCv379WLVq\nFdOmTcPT05PPP/+ciRMn0qBBA1atWmUeMKJSpUr5rmvZsiVt2rShZ8+etGrVimrVqt21Rq9UqVIM\nGzaMMWPG0KxZM06fPs306dMpWrSoeRjw8PBwrly5QkBAAP369aNv3760bdvWvI8OHTpw48YN2jbJ\nWqaUkvmP/mPsStqBNCkXQghxF9q6WnT2MpjPI1P/Mfv377d2BLPHkSU2NlZVr15dnThx4jEkyulh\n8mVkZKj09HTz3+Hh4SokJORxxlJK2dZ5zIut5du3b58KCAhQV/dfVbun7lbxS+JVenL6vR9oBbZ2\n7O5ky9lSY1PV3jV7rR0jX7Z87Gw5m1K2nc+Wsyll2/lsOZtStp3PlrMpZdv5bDmbUraV725ZLFqD\nNGHCBLp27Uq3bt1y9V25dOkS3bt3p1OnTnz44Yf39RhhWUopnnvuOaZMmUJ6ejrnzp1j6dKlNGvW\nzNrRnmp///03YWFh9OvXD4cSDiiTQuesQ+8sY7D8lzi4O6AtKZX+QgghxJNmsV/bvXv3EhMTw+LF\niwkLCyMsLCzH+okTJ/Lqq6+ydOlSdDodFy9evOdjhGVpNBqmTp3K4cOHadiwIT169CAwMJABAwZY\nO9pTa/bs2bRp0wYfHx969+6NfWl7yJDhvYUQQgghHpbFrqIiIyNp1aoVAFWqVCExMZHk5GQKFSqE\nyWTiwIEDTJ06FYAxY8YAWcMw5/eYp4W7u3uuUeWsqXbt2ixYsMDaMcRt/fv3p3///v8s0AEGMJSU\noaCFEEIIIR6GRiml7r3Zoxs9ejTNmjUzF3h69OhBWFgYHh4eJCQk0LNnT5o0acLRo0epX78+7777\n7l0fk58DBw5Y4uUIYbMy9mSg89Wh0csIdkIIIYQQ+fH19c1zudXa4dxZLlNKER8fT58+fShXrhyh\noaFs2bLlro+5m/xerKUdOHDAZrLkxZbz2XI2sO18+5L3Ud+vvrVj5MuWj50tZwPbzifZHp4t57Pl\nbGDb+Ww5G9h2PlvOBradz5azgW3lu1ulisUKSCVLlswxWebly5dxc3MDwNXVlbJly1KhQgUAGjVq\nxMmTJ+/6GCFE3rSFpCO/EEIIIcTDstiVVEBAAOvWrQPg6NGjlCxZ0tyXSK/XU758ef766y/zeg8P\nj7s+RgghhBBCCCEeN4vVINWrV49nnnmGbt26odFoGDNmDMuXL6dw4cI8++yzjBw5kuHDh6OUonr1\n6gQFBaHVanM9RgghhBBCCCGeFIv2QRo6dGiOv2vWrGn+d8WKFVm4cOE9HyOEEEIIIYQQT4p0VhBC\nCCGEEEKI26SAJIQQQgghhBC3SQFJCCGEEEIIIW6TApIQQgghhBBC3CYFJCGEEEIIIYS4TaOUUtYO\n8TjdbVZcIYQQQgghhADw9fXNc/l/roAkhBBCCCGEEA9LmtgJIYQQQgghxG1SQBJCCCGEEEKI26SA\nJIQQQgghhBC3SQFJCCGEEEIIIW6TApIQQgghhBBC3CYFJCGEEEIIIYS4TQpIwiaYTCYyMzOtHUM8\nZkaj0doRhBBCCCEeiBSQHqOrV69y7Ngxa8fI07Vr1zh+/Li1Y+TJaDSi1WrR6XQ2V1A6duwYy5Yt\ns3aMfGVkZPDXX39x8uRJa0fJZffu3bRv356oqCgAbG3KNaUU8fHxHDp0yNpR8pWYmGjtCOIJsrXP\nhHg62Pr7zpbz2XK2gsJkMlk7wn3RWzvAf8WXX37Jrl27OHnyJMWLF2fs2LHUr18fpRQajcaq2WbP\nns3OnTs5c+YM9evXZ9y4cRQuXNiqme40cOBAdDodQ4cOpXr16kDWl5DJZEKn01k126hRo3jppZfM\nfxuNRgwGgxUT5RQWFsbp06fp2LEj1apVIzk5mUKFClk7FgDTp09HKcWaNWuoU6eO1T8H/zZz5kz2\n7dvHkSNHqFmzJp9//jmlSpWydiwANmzYwKZNm0hJSSEhIYHOnTvz4osvWjvWXZlMJjQajc2dZ1tz\n529C9v9t4Xcimy1luRuTyYRWa3v3eFNSUnB2drZ2jLuy1fN78uRJqlSpYnPnNa/PrK2zpc9HWloa\nV65c4cyZM1SsWJHy5cub19ny941tHL0CLjo6mgULFtCxY0cmTZpE3bp1mTt3Lunp6VY/8dHR0Sxc\nuJCQkBCGDx/OqVOnuHjxIps2bWLOnDn8/fffVs1nNBpxcXFh27ZttG/fnvbt27Nt2zY0Gg06nY4T\nJ05w8eJFq2SLjo4mJiaGnj17AvDLL78wfPhw2rZty4QJE7h69apVcmWLiopi1apVvPPOO3To0IEl\nS5YwePBgmjZtyogRI6xaqxQVFcXJkyf57rvv2Lx5M1OnTgWyvrRt4Q5cdHQ0S5YsoXfv3oSHh6PX\n6zlx4gRr1qzhm2++4fLly1bNFhYWhpubG8HBwfj4+DBixAj8/f355ptvrJbr327cuMGZM2fYvXs3\nKSkpaLVaNBoNmZmZNnGOs9na3UqNRkNcXBybNm1i48aN3Lp1y+q/E3fSaDTEx8ezdetWtm7dmqNG\nXyll9XObXSOdffFnSy0OAD7//HOSkpJyLbeF774///yTiIiIXDXTtpANoE+fPowcOdLaMXLRaDRc\nuHCBiIgIVq9enaPpuC18JiDrWurmzZucPXuWtLQ08+fDFr7/PvnkE/r27cv06dNp3749nTt35tdf\nfwVsu8Cp++ijjz6ydoiCbvLkyfj5+fHKK69QsWJFypYtyzfffEO1atWoVKmS+c5qbGwsRYoUsWi2\njz/+mMaNG/Pqq69SvXp1Tp06xcaNG9m4cSMHDhzgiy++oFChQnh7e1s0VzadToePjw8JCQm8/fbb\nlChRgnHjxrFs2TJcXV35+OOPef755ylSpIjF7zSMGDGCpk2bEhgYyLJly5g+fTply5bF39+f3377\njRkzZlCtWjUqV65ssUx3mjNnDh4eHnTr1o0VK1Ywc+ZMAgICaNWqFdu3b2fGjBkUL16c2rVrW/zY\njRw5khYtWtC6dWu8vLxYuXIl5cqVw93d3Sa+EMePH09AQAA9evTA3d2dixcvEh4ezunTpzlw4AAz\nZszA2dnZKp+LsLAw/P39eeedd6hevTrVq1fn+vXrNGnShNWrV7N37178/f1xcHCweLZs27dvZ8qU\nKcycOZMTJ04QHh7On3/+iaenJ0WKFLH6OY6JiSE5ORkXFxdzluzvYWtbv349EyZMYNWqVZw8eZJT\np07RtGlTa8cy27BhAxMmTGDlypWcOnWKMmXKUKFCBTIzM82FYGvd9V23bh2hoaHExsaSmZlJ1apV\ncxSUrH3H/LvvvmP16tX069fPfNGcndXJycmq77+VK1cyYcIE9Ho9rVu3xmg0cvToUXQ6Hc7OzlY9\nrwDz589n3759uLq6kpqayjPPPGMT5xRg7dq1TJ48mW3btnHy5Ens7Ozw9PQkIyMDnU5n9WO3e/du\nwsPDCQsLIyYmhtWrV5OYmEi5cuWsXps5f/58du3axaRJkwgKCiIoKIjLly8THh7OqlWrqFSpEhUq\nVLBqxnwp8UgyMjLU6NGj1dSpU3MsHzlypBo5cqT57wMHDig/Pz+LZktLS1ODBw9W69atMy9r3ry5\nCgsLUxcuXFBKKfX555+rl156SSUnJ1s0WzaTyaSUUmrGjBmqY8eOKiUlRV29elXNnTtX+fr6qlq1\naqmvvvrK4rnOnTunatSooc6ePauUUqpjx45q7dq15vWpqalq+PDhatCgQRbPlm358uWqS5cuKiUl\nRfXq1StHPqWyzm2vXr1Uenq6RXOdPXtWeXp6qlu3bimllDIajWrq1KmqTZs2auPGjUoppTIzM1VG\nRoZFc2VLS0tTb7/9tpo/f7552UsvvaSmTJmibty4oZRS6osvvlCdO3e2+OciLS1NvfXWW+ZsaWlp\nSimlhg8frtauXauio6NVly5dVHh4uEVz/VtQUJBasmSJio6OVnv37lXz589XL730kvLy8lKjR49W\ncXFxVs3XqVMn1adPH/X111+rkydP5lhnrfddthYtWqiIiAh18uRJtWLFCtWkSRO1aNEipdQ/34fW\n1KJFC7Vy5Up1+vRp9c4776hhw4apXbt2qbFjx6pRo0aZvxOtYd++fSogIEANGDBADRw4UL3++uvq\np59+UkoplZ6eriIjI1VmZqbKzMy0Sr5mzZqpDRs2KKWUWr16terXr59q166datOmjfrggw/U+fPn\nrZJLKaUaN26sfv31V6WUUmvXrlVdu3ZVwcHByt/fXw0aNMiq51UppQICAtTevXvV/v37Va9evdTf\nf/9t1Tx3atGihVq7dq06f/68+t///qdef/11FRERoUaMGKFGjx6tzpw5Y9V8zZs3V3PmzFF79uxR\n69atU507d1aBgYGqV69e6qefflKpqalW+27p0qWLWrFiRa7lp06dUsOHD1chISFqz549Vkh2b1KD\n9Ii0Wi2XLl1iyZIltGjRwnzH0s3NjXnz5tG2bVscHR0ZNWoUTZs2JSAgwGLZdDodBw4c4LfffqND\nhw4kJyfz559/Mn78eAoXLozJZKJy5cqsWrUKT09PypYta7Fs2bLvuDRs2JAjR45w4sQJmjdvTt26\ndVm2bBlBQUEsWLAAJycn6tata7Fcx44d4+eff2bnzp2cOnUKOzs7unTpYu7fo9frKV26NBEREdSr\nV4/ixYtbLFu24sWLs3nzZq5fv07lypUpUaIEHh4e5vXVq1dn0aJF1KxZ06Lnds2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CAAAI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\nrpSZUAAAAABJRU5ErkJggg==\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"numpy.set_printoptions(suppress=True, linewidth=200)\n",
"\n",
"def evaluate_models():\n",
" sizes = numpy.arange(2, 21).astype('int')\n",
" n, m = sizes.shape[0], 20\n",
" \n",
" skl_predict, pom_predict = numpy.zeros((m, n)), numpy.zeros((m, n))\n",
" skl_fit, pom_fit = numpy.zeros((m, n)), numpy.zeros((m, n))\n",
" skl_error, pom_error = numpy.zeros((m, n)), numpy.zeros((m, n))\n",
" \n",
" for i in range(m):\n",
" for j, size in enumerate(sizes):\n",
" X, y = create_dataset(50000, size, 2)\n",
" \n",
" pom = GeneralMixtureModel(MultivariateGaussianDistribution, n_components=2)\n",
" skl = GMM( n_components=2, n_iter=1 )\n",
" \n",
" # bench fit times\n",
" tic = time.time()\n",
" skl.fit( X )\n",
" skl_fit[i, j] = time.time() - tic\n",
"\n",
" tic = time.time()\n",
" pom.fit( X, max_iterations=1 )\n",
" pom_fit[i, j] = time.time() - tic\n",
"\n",
" # bench predict times\n",
" tic = time.time()\n",
" skl_predictions = skl.predict( X )\n",
" skl_predict[i, j] = time.time() - tic\n",
"\n",
" tic = time.time()\n",
" pom_predictions = pom.predict( X )\n",
" pom_predict[i, j] = time.time() - tic\n",
" \n",
" # check number wrong\n",
" skl_e = (y != skl_predictions).mean()\n",
" pom_e = (y != pom_predictions).mean()\n",
"\n",
" skl_error[i, j] = min(skl_e, 1-skl_e)\n",
" pom_error[i, j] = min(pom_e, 1-pom_e)\n",
" \n",
" fit = skl_fit / pom_fit\n",
" predict = skl_predict / pom_predict\n",
" plot(fit, predict, skl_error, pom_error, sizes, \"dimensions\")\n",
"\n",
"evaluate_models()"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": true
},
"source": [
"It seems as though both fitting and prediction using pomegranate scale less well than sklearn to more dimensions, but that it is stil faster. \n",
"\n",
"This notebook tested a main portion of the overlap between sklearn and pomegranate, but both offer clustering options which aren't displayed here. pomegranate allows any distribution or mixture of distributions, univariate or multivariate, and even some more complex models to be used as a component in the mixture model. The out of core API which pomegranate offers also extends to GMMs, allowing them to be trained using exact EM updates on data which can't fit in memory. In contrast, sklearn offers suppoort for both dirichlet process GMMs (DPGMMs) and variational Bayes GMMs (VBGMMs) as well, which are robust clustering models.\n",
"\n",
"We hope this has been useful to you! If you're interested in using pomegranate, you can get it using `pip install pomegranate` or by checking out the github repo."
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.12"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
pomegranate-0.13.5/benchmarks/pomegranate_vs_sklearn_naive_bayes.ipynb 0000664 0000000 0000000 00001652741 13740675601 0026411 0 ustar 00root root 0000000 0000000 {
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# pomegranate / sklearn Naive Bayes comparison\n",
"\n",
"authors: \n",
"Nicholas Farn (nicholasfarn@gmail.com) \n",
"Jacob Schreiber (jmschreiber91@gmail.com)\n",
"\n",
"sklearn is a very popular machine learning package for Python which implements a wide variety of classical machine learning algorithms. In this notebook we benchmark the Naive Bayes implementations in pomegranate and compare it to the implementation in sklearn."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"scrolled": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Populating the interactive namespace from numpy and matplotlib\n"
]
}
],
"source": [
"%pylab inline\n",
"import seaborn, time\n",
"seaborn.set_style('whitegrid')\n",
"\n",
"from sklearn.naive_bayes import GaussianNB\n",
"from pomegranate import *"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Lets first define a function which will create a dataset to train on. We want to be able to test a range of datasets, from very small to very large, to see which implementation is faster. We also want a function which will take in the models and evaluate them. Lets define both of those now."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"def create_dataset(n_samples, n_dim, n_classes):\n",
" \"\"\"Create a random dataset with n_samples in each class.\"\"\"\n",
" \n",
" X = numpy.concatenate([numpy.random.randn(n_samples, n_dim) + i for i in range(n_classes)])\n",
" y = numpy.concatenate([numpy.zeros(n_samples) + i for i in range(n_classes)])\n",
" return X, y\n",
"\n",
"def plot(fit, predict, skl_error, pom_error, sizes, xlabel):\n",
" \"\"\"Plot the results.\"\"\"\n",
" \n",
" idx = numpy.arange(fit.shape[1])\n",
" \n",
" plt.figure(figsize=(14, 4))\n",
" plt.plot(fit.mean(axis=0), c='c', label=\"Fitting\")\n",
" plt.plot(predict.mean(axis=0), c='m', label=\"Prediction\")\n",
" plt.plot([0, fit.shape[1]], [1, 1], c='k', label=\"Baseline\")\n",
" \n",
" plt.fill_between(idx, fit.min(axis=0), fit.max(axis=0), color='c', alpha=0.3)\n",
" plt.fill_between(idx, predict.min(axis=0), predict.max(axis=0), color='m', alpha=0.3)\n",
" \n",
" plt.xticks(idx, sizes, rotation=65, fontsize=14)\n",
" plt.xlabel('{}'.format(xlabel), fontsize=14)\n",
" plt.ylabel('pomegranate is x times faster', fontsize=14)\n",
" plt.legend(fontsize=12, loc=4)\n",
" plt.show()\n",
" \n",
" \n",
" plt.figure(figsize=(14, 4))\n",
" plt.plot(1 - skl_error.mean(axis=0), alpha=0.5, c='c', label=\"sklearn accuracy\")\n",
" plt.plot(1 - pom_error.mean(axis=0), alpha=0.5, c='m', label=\"pomegranate accuracy\")\n",
" \n",
" plt.fill_between(idx, 1-skl_error.min(axis=0), 1-skl_error.max(axis=0), color='c', alpha=0.3)\n",
" plt.fill_between(idx, 1-pom_error.min(axis=0), 1-pom_error.max(axis=0), color='m', alpha=0.3)\n",
" \n",
" plt.xticks(idx, sizes, rotation=65, fontsize=14)\n",
" plt.xlabel('{}'.format(xlabel), fontsize=14)\n",
" plt.ylabel('Accuracy', fontsize=14)\n",
" plt.legend(fontsize=14) \n",
" plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Lets look first at single dimension Gaussian datasets. We'll look at how many times faster pomegranate is, which means that values > 1 show pomegranate is faster and < 1 show pomegranate is slower. Lets also look at the accuracy of both algorithms. They should have the same accuracy since they implement the same algorithm."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"sizes = numpy.around(numpy.exp(numpy.arange(8, 16))).astype('int')\n",
"n, m = sizes.shape[0], 20\n",
"\n",
"skl_predict, pom_predict = numpy.zeros((m, n)), numpy.zeros((m, n))\n",
"skl_fit, pom_fit = numpy.zeros((m, n)), numpy.zeros((m, n))\n",
"skl_error, pom_error = numpy.zeros((m, n)), numpy.zeros((m, n))\n",
"\n",
"for i in range(m):\n",
" for j, size in enumerate(sizes):\n",
" X, y = create_dataset(size, 1, 2)\n",
"\n",
" # bench fit times\n",
" tic = time.time()\n",
" skl = GaussianNB()\n",
" skl.fit(X, y)\n",
" skl_fit[i, j] = time.time() - tic\n",
"\n",
" tic = time.time()\n",
" pom = NaiveBayes.from_samples(NormalDistribution, X, y)\n",
" pom_fit[i, j] = time.time() - tic\n",
"\n",
" # bench predict times\n",
" tic = time.time()\n",
" skl_predictions = skl.predict(X)\n",
" skl_predict[i, j] = time.time() - tic\n",
"\n",
" tic = time.time()\n",
" pom_predictions = pom.predict(X)\n",
" pom_predict[i, j] = time.time() - tic\n",
"\n",
" # check number wrong\n",
" skl_e = (y != skl_predictions).mean()\n",
" pom_e = (y != pom_predictions).mean()\n",
"\n",
" skl_error[i, j] = min(skl_e, 1-skl_e)\n",
" pom_error[i, j] = min(pom_e, 1-pom_e)\n",
"\n",
"fit = skl_fit / pom_fit\n",
"predict = skl_predict / pom_predict\n",
"\n",
"plot(fit, predict, skl_error, pom_error, sizes, \"samples per component\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"It looks as if pomegranate is approximately the same speed for training small models but that the prediction time can be a lot faster in pomegranate than in sklearn.\n",
"\n",
"Now let's take a look at how speeds change as we increase the number of classes that need to be predicted rather than phrasing all of the comparisons on binary classification."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"sizes = numpy.arange(2, 21).astype('int')\n",
"n, m = sizes.shape[0], 20\n",
"\n",
"skl_predict, pom_predict = numpy.zeros((m, n)), numpy.zeros((m, n))\n",
"skl_fit, pom_fit = numpy.zeros((m, n)), numpy.zeros((m, n))\n",
"skl_error, pom_error = numpy.zeros((m, n)), numpy.zeros((m, n))\n",
"\n",
"for i in range(m):\n",
" for j, size in enumerate(sizes):\n",
" X, y = create_dataset(50000 // size, 1, size)\n",
"\n",
" # bench fit times\n",
" tic = time.time()\n",
" skl = GaussianNB()\n",
" skl.fit(X, y)\n",
" skl_fit[i, j] = time.time() - tic\n",
"\n",
" tic = time.time()\n",
" pom = NaiveBayes.from_samples(NormalDistribution, X, y)\n",
" pom_fit[i, j] = time.time() - tic\n",
"\n",
" # bench predict times\n",
" tic = time.time()\n",
" skl_predictions = skl.predict(X)\n",
" skl_predict[i, j] = time.time() - tic\n",
"\n",
" tic = time.time()\n",
" pom_predictions = pom.predict(X)\n",
" pom_predict[i, j] = time.time() - tic\n",
"\n",
" # check number wrong\n",
" skl_e = (y != skl_predictions).mean()\n",
" pom_e = (y != pom_predictions).mean()\n",
"\n",
" skl_error[i, j] = min(skl_e, 1-skl_e)\n",
" pom_error[i, j] = min(pom_e, 1-pom_e)\n",
"\n",
"fit = skl_fit / pom_fit\n",
"predict = skl_predict / pom_predict\n",
"\n",
"plot(fit, predict, skl_error, pom_error, sizes, \"number of classes\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"It looks like, again, pomegranate is around the same speed as sklearn for fitting models, but that it is consistently much faster to make predictions."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"1.57 ms ± 38.4 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)\n",
"672 µs ± 11.3 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)\n"
]
}
],
"source": [
"X, y = create_dataset(50000, 1, 2)\n",
"skl = GaussianNB()\n",
"skl.fit(X, y)\n",
"\n",
"pom = NaiveBayes.from_samples(NormalDistribution, X, y)\n",
"\n",
"%timeit skl.predict(X)\n",
"%timeit pom.predict(X)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This does show that pomegranate is faster at making predictions but that both are so fast that potentially it doesn't really matter.\n",
"\n",
"While it's good to start off by looking at naive Bayes' models defined on single features, the more common setting is one where you have many features. Let's look take a look at the relative speeds on larger number of examples when there are 5 features rather than a single one.\n"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
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Cl1xyCa+8Un8rvaN9AwwaNIgOHTrQqVOnxKAkezOjKe0pm4NS6gjgDq31id70eACt9d1JaR4DlmitJ3rp/6i1PjJtO3cBjtb6lrT5vYH3gG5aa8eruTpkZ4KrsrIyp0+fPrt2gM1s4TcbeO/vZXQ9oLTF9lG7NUp1ZYSs9gEOPq6EbvvkNjr6jnCVlZWRKX8jwiVlkpmkXDKPlElmas5ykTJuHtXV1Y32txLbqqmpYfDgwdx6662cdtppLbaf1i6X7X2f5s2bN2/gwIGHNLSsNZsFdgbKk6ZXAIPS0twBvK2UugbIBn7awHbOBhoaPP9c3Jqq5GjxF0qpwcC3wPVa6/IG1ttrBbMtgtkWNRvr+GRKOV93C3PwcaV07pr5nV+FEEIIIUTbsW2byspKnn76aYLBICeddFJbZykjtGZwZTQwL73a7Fzgaa31H72aq2eVUgdqrW0ApdQgoEpr/VUD2zoHuCBp+nXgBa11rVJqFG5frqHby2BtbS1lZWVNPJyWtXJ5HdFojMrKta2zw1xYtXQL5Q+tJreHn30ODlFQKINJpqupqcmYvxHhkjLJTFIumUfKJDM1Z7lEIhGqq6ubZVt7M8dx5PfYBCtXruSUU06htLSUO+64g1gs1qK/t9Yul0gkskvfzda8e14BdE2a7gKkD/dyGXASgNZ6llIqBBQD8Vc/nwO8kL5hpVQ/wNJaz4vP01onRyWPAxN3lMFgMJgx1emWsYHFVhnFxe1ab6fFgO2wpaKW79536HRwDgcf2Z6CQnlHVpw0ucg8UiaZScol80iZZKbmbhYozdl+PGkW2DT77rsvWutW219rl4vf799es8BG12vNDjZzgN5KqZ5KqQBuoDQtLc1y4HgApVQfIASs8aZNYAQwpYFtn0ta0KWU6pg0eRogj+uawjTI6RAir2uI1Qs2MeOvi/nv+9+zdcu2w4MKIYQQQggh6rVazZXWOqqUGgO8hTvM+lNa66+VUncCc7XW04AbgceVUtfjNhm8OKkP1WBghda6oeFPzgJOTpt3rVLqNCAKrAMubvaD2oOZPoPcTmHsiMPS2etYNnc9vY9uxwED2hEMSnNBIYQQQggh0rXqXbLWejru8OrJ8yYkfV4AHNXIuh8AhzeybJ8G5o0Hxv+I7ArA9BvkdQ0TrbHRH1SyePY6+hzbnv0OKsKyZGRBIYQQQggh4uTuWDSJFTLJ7xbGn+3ji+k/MO2xhSz8Zj2xmN3WWRNCCCGEECIjSHAldkogy6KgRxaGz2DO1JW8+cwSypdubutsCSGEEEII0eak84zYJcFci2CuRfX6Oj6avJzCnmH6DymlQ6fsts6aEEIIIYQQbUJqrsSPEi4MUNAtxJaKOt57einvvrqMdWtr2jpbQgghhBBCtDoJrsSPZxpktw+Q3yXE2sVbeetvi/nP2yvZtEmGbxdCCCGEaEmvvPIK/fv3b+tsCI80CxTNxvAZ5HQMYUcdVs7fyIr5G9nniCIOOqSYcFj+1IQQQgixd4hEIvj9/rbOxh6hrq6OQCDQ1tloMqm5Es3OtAxyO4fIbh9g8X/W8voj3zJ/7hoidbG2zpoQQgghMswFF1zAhAkT+N3vfsehhx7KoYceysSJE7Ht+hGJN27cyNixYzn00EPp27cvF198MQsXLkwsj9fezJw5k5NOOol+/foxatQoNm/ezIwZMzjhhBMYOHAgN910EzU19d0XHMfh8ccf56c//Sl9+/Zl2LBhvPnmmyn5+/zzz/n5z3/OQQcdxBlnnMHMmTNRSjF79mwAZs+ejVKKmTNncuaZZ3LggQfyn//8h+XLlzN69GiOOuooDj74YH7+85/z/vvvp2x76NChPPLII0yYMIEBAwYwePBgnnjiiZQ0kyZNYtiwYRx88MEcc8wx3HLLLWzatCmx7/Hjx1NVVYVSCqUUDz30EOAGJffeey+DBw/m4IMP5he/+AUfffTRdsviww8/ZOTIkRx66KEcdthhXHbZZSxevDglzerVq7nxxhsZNGgQ/fr14/TTT+e///1vYvkHH3zAiBEj6Nu3L4MGDWLUqFHU1tYmjvfJJ5/cpvzvvPPOlN/JQw89xPjx4znkkEP49a9/DcCDDz7IiSeeSN++fRk6dCj33HNPYrs72vfDDz/Mqaeeus3xnnPOOfzud7/b7u9kZ0l1gmgxvoA7fHu0OsaCtytYPGsd+w8p5if7F+LzSVwvhBBCCNfrr7/O8OHDmTJlClprbrvtNkpKSrjkkksAGDduHN999x2PPPIIeXl5PPDAA1x++eW89dZbhEIhwA0mJk2axH333UckEuGaa67h2muvJRgM8uc//5kNGzZwzTXX8Pzzz3PppZcC8Kc//YkZM2YwYcIEevbsyfz587n11lspLi5myJAhbN26lauuuoqjjjqKe+65h4qKCu66664Gj+G+++5j7NixdO/enezsbCoqKhg8eDDXXXcdoVCI6dOnc8011/Daa6/Rq1evxHrPPPMM11xzDa+++ioffvghv/vd7xg4cGCiqZ9hGNx888107dqVVatW8dvf/pbf/va33HvvvfTv35+bb76ZBx54gHfeeQeArKwsAMaPH095eTl//OMf6dChAzNnzmT06NG8/PLL7Lfffg0eQ3V1NRdddBFKKWpqanj00UcZNWoUb775JoFAgKqqKi644AKKiop4+OGHKS0t5Ztvvkms/+GHH3L11VdzxRVXcPfddxONRvn4449TAuWmmDRpEqNHj2bq1Kk4jgNAOBzmrrvuorS0lMWLF3P77bcTCAS47rrrdrjvM888k0ceeYQvvviCvn37ArBkyRI+++wz7rjjjp3K245IcCVanBX2UdA9TO3WKJ+9/gPffLKWfkNL6NErD9OUIEsIIYRoCVs+38Lmz1r3dSm5/XPJ6Zez0+uVlJRw6623YhgGvXr1YunSpUyaNIlLLrmEpUuX8t577/Hcc89x6KGHAnDvvfcyZMgQXn/9dUaMGAFANBplwoQJ7LPPPgAMGzaMp59+mo8//piioiIAjj/+eGbPns2ll15KVVUVkyZN4qmnnuKQQw4BoGvXrnz66adMnjw5sX3btvn9739PKBSid+/ejBo1KlGbkmzMmDEcffTRiemioqKUIGb06NG8//77vPXWW1x99dWJ+UcddRTnn38+4NbiPPvss8yaNSsRXF188cWJtF26dOGmm27i6quvZuLEiQQCAXJzczEMg/bt2yfSLV++nDfffJP33nuPTp06AXD++efzySefMGXKlEYDihNPPDFl+u6772bgwIF88cUXHHLIIbzxxhusWbOGKVOmJH6n3bp1S6R/5JFHOPHEE7n++usT8xoL5LbnsMMO44orrkiZd+WVVxIOhxO/h6uuuoqnnnoqEVxtb9/hcJhjjjmGl19+ORFcTZ06lQMOOGCX8rc9ElyJVhPMtghmW9RsjDBrygoWdAvTf2gpnbvu/ElYCCGEEHuOfv36YRhGYrp///48+OCDbNmyhcWLF2OaJgcffHBieW5uLj/5yU9YtGhRYl4gEEgEVgDt2rWjuLg4EQTE58XXWbRoEbW1tVx++eUp+45EInTu3Blwazd69+6dqB2L57UhBx54YMp0VVUVDz/8MB988AFr1qwhGo1SW1uLUiolXfp0SUkJ69atS0zPmjWLv/3tbyxevJjNmzdj2zaRSIQ1a9ZQWlraYF6+/vprHMfhlFNOSZlfV1fH4Ycf3uA64AZlDz74IJ9//jnr1q3DcRxs2+b7778HYMGCBSilUn6nycrKyhg+fHij22+q9N8lwDvvvMMLL7zA8uXLqaqqIhaLpdSI7WjfI0aMYNy4cdx88834/X5ee+21lCC3uUhwJVpdKN9PKN9PVWUdH/59Ke1ULgcf056S0qy2zpoQQgixx8jpl7NLtUiZJt4srCHJQZFlWdssSx9UwjCMxA15fLuPPvpoonYHoKamhpycnESa5H1sT7xWJW7ixIl89NFHiaaC4XCYsWPHEolEUtI1lO94HleuXMlVV13FWWedxbXXXktBQQELFizghhtu2GY7yeL5fvnll7fZfnKgmG7UqFGUlpZy5513Ulpais/n45RTTknsa3tl0RSGYWyzjYaOI/13OX/+fMaNG8cvf/lLjjnmGPLy8njvvfeYOHFik/c9ZMgQQqEQb731Frm5uWzevLnBflg/lrTJEm0mqzhAfrcwG5ZV8e6T3/HBm+VsWC/vyBJCCCH2Np9//nnKTff8+fMpKSkhJyeHfffdF9u2mT9/fmL5li1b+Pbbb1P6Lu2sXr16EQgEWLVqFd27d0/869atW6LmqlevXnz77bcpg2B88cUXTdr+p59+yhlnnMGJJ57IfvvtR4cOHVi+fPlO5fGrr74iEokwfvx4+vfvT8+ePamoqEhJ4/f7icVSBw3r06cPjuOwZs2alGPr3r17o7Vd69evZ/HixVx11VUceeSR9OrVi61btxKNRhNpDjjgALTWKTVr6fudNWtWo8dTVFTEmjVrEtO1tbV89913O/w9fPrpp5SUlPDLX/6Svn370qNHD1atWrVT+7Ysi+HDhzN16lSmTp3Kz372M/Ly8na4750lwZVoW6ZBTocgeV1CrF6wiRl/Xcys91axdYu8I0sIIYTYW1RUVPD73/+eJUuWMGPGDJ588slEX6MePXpw/PHHM2HCBObOnYvWml//+tfk5OQwbNiwXd5nTk4Ol156Kffccw8vv/wyy5Yto6ysjJdeeol//OMfgNtvyzRNbr31VhYtWsQnn3zCY489BrDDGq0ePXrwzjvv8PXXX6O15qabbtpmdLsd6d69O7Zt88wzz1BeXs4bb7zBM888k5Kmc+fO1NbW8vHHH7Nu3Tqqq6vp2bMnw4YNY/z48cyYMYPy8nK+/PJLnnzySd5+++0G95Wfn09hYSEvvfQSy5Yt43//+x+33357Ss3XqaeeSrt27fjlL3/J3LlzKS8v5913302MFjh69GhmzJjBAw88wKJFi1i4cCFPP/001dXVABx++OG8/vrrzJ49m4ULF3LzzTdvtwYu+XdZUVHBtGnTKC8v5/nnn+eNN95ISbOjfYPbNHDOnDl88MEHnHnmmU0rhJ0kwZXICIbPILdTmJyOIZb9bz1vPLqIeZ+spqYmuuOVhRBCCLFbGzZsGLZtc9ZZZ3Hbbbdx5plnpgzkcPfdd9O3b19Gjx7NiBEjqKmp4YknnthuE7emuO666xgzZgxPPfUUp5xyCpdccgn//ve/6dKlCwDZ2dn89a9/ZdGiRZxxxhncc889jBkzBoBgMLjdbY8bN4527dpx3nnnccUVV9CvX7/EwBlNtd9++3HLLbcwadIkTjnlFF566SV+85vfpKQZMGAA55xzDjfccANHHHFEYij3u+++m+HDh3Pvvffyf//3f4waNYo5c+akNIFMZpomDzzwAFprTj31VO68805+9atfpbxjKisri+eee47S0lJGjRrFqaeeykMPPZQINI899lgefvhhPvroI8444wzOP/98/vvf/yYGMLvqqqs4/PDDufrqq7n00ksZMGAABxxwwA5/D0OHDuWiiy7irrvu4rTTTuOTTz7h2muvTUmzo32DO2DJoYceSseOHRk0aFATSmDnGT+27eSepKyszOnTp09bZwOAhd9s4L2/l9H1gIarbvd00RqbrRW1WGGTPse2Z7+DirCstn8WUFZWRqb8jQiXlElmknLJPFImmak5y2V3LeMLLriA3r17M2HChLbOCuAOR57e5yfZv//9b8aMGcMnn3zS6MAOovntqFya6uSTT2bYsGGMHj16u+m2932aN2/evIEDBzYYKcuAFiIjWSH3HVmR6hhfTv+Bbz9Zy0HHl7BP73x5R5YQQgghWs2rr75K165d6dChAwsXLuSuu+7iuOOOk8BqN7N27VreeOMNVq5cydlnn91i+2nV4EopdRLwIOADntBa/yFteTfgGaDASzNOaz1dKXUecFNS0r7AAK31fKXUB0BHIN6g8gStdYVSKgj8HRgIrAXO1lovbbGDEy3CH/aR3yOL2s1R5kxdyYIOa+k/tJRuPXPbOmtCCCGE2AtUVlby0EMPUVFRQfv27Tn22GMbfM+VyGxHHnkkhYWF/L//9/9aNDButeBKKeUD/gL8DFgBzFjA0rkAACAASURBVFFKTdNaL0hKdivwotb6UaXU/sB0oIfWejIw2dvOQcBrWuv5Seudp7Wem7bLy4D1Wut9lVLnABOBlgtTRYsK5loEcy2q19fxn+eXU9gzTP8hpXTolN3WWRNCCCHEj/Dss8+2dRa264orrtjmhbZi96O1bpX9tGb7qsOARVrrJVrrOmAKcHpaGgeIj4mYD6xiW+cCLzRhf6fj1oIBvAwcr5Rq2osKRMYKFwYo6BZiS0Ud701ayruvLmPdWhm+XQghhBBCtL3WbBbYGShPml4BpA/TcQfwtlLqGiAb+GkD2zmbbYOySUqpGDAV+J3W2knen9Y6qpTaCLQDKn/kcYi2Zhpktw/gFDlULt7KW98spsuAfPodUUJeXmDH6wshhBBCCNECWjO4aqjWKH2ownOBp7XWf1RKHQE8q5Q6UGttAyilBgFVWuuvktY5T2u9UimVixtcXYDb16op+0tRW1tLWVlZEw+nZa1cXkc0GqOycm1bZyWz+cE2bMo+2sSCmeWU9AvSUwUJBlumUrampiZj/kaES8okM0m5ZB4pk8zUnOUSiUTYunVrytDTYuc5jpPybiSRGVqzXGzbJhKJ7NJ3szWDqxVA16TpLmzb7O8y4CQArfUspVQIKAbir6I+h7QmgVrrld7PzUqp53GbH/49aX8rlFIWbjPDhl8n7QkGgxkzhKllbGCxVUZxcbu2zsruoQPE6my2LKnl2xUGPzm2mD4HFRIMNu+f+O46zO2eTMokM0m5ZB4pk8zUnOWyfPly1q1bR2lpKX6/f4cvuRUNa64hv0Xzao1ycRyHSCRCZWUlBQUFdOvWrcF08+bNa3QbrRlczQF6K6V6AitxA6WRaWmWA8cDTyul+gAhYA2AUsoERgCD44m9oKlAa12plPIDpwL/9hZPAy4CZgFnAu95zQXFHsoXcIdvj9bEKHu7gkWfrOWA49rzk/0LZfh2IYQQe7wuXbpQWVnJsmXLiEajbZ2d3VYkEsHv97d1NkSa1ioXy7LIz8+nuLh419Zv5vw0yuv3NAZ4C3eY9ae01l8rpe4E5mqtpwE3Ao8rpa7HbcJ3cVJANBhYobVekrTZIPCWF1j5cAOrx71lT+I2K1yEW2N1TgsfosgQVshHfvcwtVujfPb6D3zzyVr6HteenvvmS1MJIYQQeyzTNCkpKaGkpKSts7Jbk1rezLS7lEurvudKaz0dd3j15HkTkj4vAI5qZN0PgMPT5m3FfY9VQ+lrcGu6xF4qmG0RzLao2Rhh9osrKeu6jv5DS+ncNaetsyaEEEIIIfZArRpcCdEWQvl+Qvl+qirrmPnMUtr9JIf+x5ZQUprV1lkTQgghhBB7EGkjJfYaWcUBCrqH2VhezbtPfscHb5SzYb28I0sIIYQQQjQPqbkSexfTIKdDECfmsLpsM//6chPdDyuk36BisnPkHVlCCCGEEGLXSXAl9kqGzyC3Uwg74rB8znrKP91Ar6PaceCAdoRC8rUQQgghhBA7T+4ixV7N9BvkdQ0TrbFZOLOS72avo8+Q9ux3UBGWJa1mhRBCCCFE08ndoxCAFXLfkRXItfhy+g9Me2wh35atJxaz2zprQgghhBBiNyHBlRBJ/GEf+T2yMCyDea+s5I2nl7D8u83YtgRZQgghhBBi+6RZoBANCOZYBHMsqtfX8Z/nl1PQM0z/Y0vbOltCCCGEECKDSXAlxHaECwOE8x22VtTx/tNLsQu3EqupJL8wSH5RkJwcC9OUCmAhhBBCCCHBlRA7Zhpktw/gFDms+m4zX761Ghxvkd8gqzhIYacQRR1C5BcGySsIkJ0tQZcQQgghxN5GgishmsjwGQQLfOQXhxPz7KhDpDrGqi83UT5vAxiAA2bAJLckSEGnEO06hMnN91NQGCQr2992ByCEEEIIIVqUBFdC/AimZRDMtQjmpn6V7IhDzeYIKz6rYVlkPYZp4NgOVtgkpzRIYYcwRR1C5OUHyC8MEg7LV1EIIYQQYncnd3RCtADTbxDK90N+ak1VrM6men0dm1bWsDTqti10HLCyfeSVBinsFKawfYi8ggD5BQF5obEQQgghxG5E7tyEaEW+gIkvECCUnzo/WmOzZU0tG5ZVszjmJJoXBnIt8joGKeoYprA4RG5BgIKCAP6Ar03yL4QQQgghGifBlRAZwAqZWKEAFKbOj9bE2Ph9DWsXb8WxwTDc5oXBAj95HYK06xSmoCjoBl2FQSxLBtEQQgghhGgrElwJkcGskA8r5EsNumyHaK3NhuXVVOot7sCFDmBAuChAfocgRZ3DFHgjF+blB/D5JOgSQgghhGhprRpcKaVOAh4EfMATWus/pC3vBjwDFHhpxmmtpyulzgNuSkraFxgAfAu8BPQCYsDrWutx3rYuBu4FVnrrPKy1fqKFDk2I1mMaWGEfVjitaaDtUFcTY+13Vawu24wTb11oGGS185PfIURRp3jQ5Sc3T4IuIYQQQojm1GrBlVLKB/wF+BmwApijlJqmtV6QlOxW4EWt9aNKqf2B6UAPrfVkYLK3nYOA17TW85VSWcB9Wuv3lVIB4F2l1P9prf/lbe8fWusxrXSIQrQt0yCQZRHISp3txNyga82irXz/1SYMx6vo8rnv7yroFKKo1HtHV6G8GFkIIYQQYle1Zs3VYcAirfUSAKXUFOB0IDm4coA873M+sKqB7ZwLvACgta4C3vc+1ymlPgW6tEjuhdhNGT6DYLZFMDt1vh1z39H1/YItrPhsIwYGDg6mZZDdPkhBR3kxshBCCCHEzmjN4KozUJ40vQIYlJbmDuBtpdQ1QDbw0wa2czZuUJZCKVUADMNtdhj3C6XUYNzmg9drrcvT1xNib2X6DII5FsGc1Pn1L0beSPncDWACDviCJjklbtBV3DFMbr47XLy8GFkIIYQQwtWawZXRwDwnbfpc4Gmt9R+VUkcAzyqlDtRa2wBKqUFAldb6q+SVlFIWbm3Wn+M1Y8DrwAta61ql1CjcvlxDt5fB2tpaysrKdvrAWsLK5XVEozEqK9e2dVZEkmg0sveUiUXKGaI2arNpmcOKbx2cCGC4o2iYAYNQO5PsYh+5hRZZOSbZOSbBYOvUctXU1GTM91bUk3LJPFImmUnKJfNImWSm3aVcWjO4WgF0TZruwrbN/i4DTgLQWs9SSoWAYqDCW34OXpPANH8DFmqt/xSfobVOvgN+HJi4owwGg0H69Omzo2StwjI2sNgqo7i4XVtnRSSprFwrZZImVmcTqY4SWWlTudTBMOIvRjbI6xCksFMWRe1D5BX4yS8IEAw272mnrKwsY763op6US+aRMslMUi6ZR8okM2VSucybN6/RZa0ZXM0BeiuleuKO4HcOMDItzXLgeOBppVQfIASsAVBKmcAIYHDyCkqp3+H2z7o8bX5HrfX33uRpQOaHukLshrb7YuSKWjYsrWax7bgjFzoQzLPI7SAvRhZCCCHEnqdJwZVS6k+4Q6d/tcPEjdBaR5VSY4C3cIdZf0pr/bVS6k5grtZ6GnAj8LhS6nrcJoMXa63jTQcHAyuSmv2hlOoC3AJ8A3yqlIL6IdevVUqdBkSBdcDFu5p3IcTOa9KLkWP184MFfvI7hijqGKKwnTtyYV5+QF6MLIQQQojdRlNrrg4FrlFKzQOeAKZorTft7M601tNxh1dPnjch6fMC4KhG1v0AODxt3goa7suF1no8MH5n8yiEaFmNvRg5UmuzflkVa77ZHH8nMg6Q1S5AXqm8GFkIIYQQma9JwZXW+ijlVgtdCtwO3K+UegV4Ums9syUzKITYC5gG/rAP/w5ejIztznbM+hcjb41WkxPeTH6RvKNLCCGEEG2ryX2utNYaGKuUGg+cjBtova2UWg48CfxNa72uZbIphNgrNeHFyOsqatmsy3EcB9Nvuv25OoUT7+gqKGz+QTSEEEIIIRqyK3ccftwX/ebj9p1aDlwA3KqUulJr/Xwz5k8IIbaR/GLkasMirzgEgB1xqNkYYdn3NXwXcRJtC4MFfgo6hWjXJUxhUYj8wgC5eX6p5RJCCCFEs2pycKWUOgS3tuocoAr3vVGXa62/85b/CngAkOBKCNEmTL9BKN9PKD/pxcZef651S6uo+GYzOG5fLtNnkF0SpKhLmOKOYfIKAhQUBQmFpJZLCCGEELumqaMFfgko3JH+Lgbe1FrH0pI9jxtcCSFE5mikP5cddYhUx1jx2QaW/W994v1cwTyLvI5uLVdRcUgG0BBCCCFEkzX1Ee2LuEOnr2wsgdZ6DSB3H0KI3YJpGQRzLYK5qafBaE2MDSurqfx2iztqoQP4DLLbByjsHKZ956xELVc4LLVcQgghhKjX1DuDiTQQOCmlQoCtta5r1lwJIUQbSQwVX1Q/z445RKpirPpyI+XzNmCYBo7t4M+2yOsUpF2nMEXtQ+QXBckvkFouIYQQYm/V1ODqJWAmcH/a/FHAEOCMZsyTEEJkFNPXWC2XzaYf3Bci47i1XI5pkN3eT2HnMO06hikoClJQGCQr29/I1oUQQgixp2hqcHUUcEsD898Bbm6+7AghxO7DCplYoUDKC5Hjw8R/v2ALKz7dmOjLZYVN8jqGKOqSRbv2IfIKAxQUBrEsqeUSQggh9hRNDa6ygGgD820gt/myI4QQu7fkYeKTxWpttqypZf2yKhZ5wwEZpkG4yE9+xxDtu4TJLwySXxQkNzfQ+hkXQgghxI/W1ODqC+Bc4Pa0+SOBr5o1R0IIsQfyBU3CwQDhBmq51izayvdfbXLHiAd8IfdlyO26ZFFUEia/MEBBQQB/wNfwxoUQQgiREZoaXP0W+KdSal/gPW/e8cAI4OctkTEhhNjTNVrLVWdTva6O78prWGw7GIaB4+DWcnlBV2GRW8uVk2PJy5CFEEKIDNGk4Epr/aZSahhwK/Bnb/ZnwGla63+1VOaEEGJv5AuY+AIBQgVJM223lqtySRU/LNicqOUyA24tV1EndwCN/MIA+QUBgkEZJl4IIYRobU2++mqtZwAzWjAvQgghGmMaBLIsAlmps+2IQ83GCMu+r+G76DoMvJchF/gp6OS+DLmwKER+YYDcPL/UcgkhhBAtSB5tCiHEbsz0G4Ty/YTyk4Z6tx0itTbrllaxumyzO0S84b44OackSGHnMMUdw4mXIYdCcikQQgghmkOTrqhKqQDuUOznAt2AlBe2aK2ll7UQQmQK08Af9uEPp56a7ahDXVWMFZ9tYNn/1ieGiQ/mWeR1CtGuc5ii4ngtl7wMWQghhNhZOzOgxdnA3cADwE1AD+Ac4Lam7kwpdRLwIOADntBa/yFteTfgGaDASzNOaz1dKXWet8+4vsAArfV8pdRA4GkgDEwHfqW1dpRSRcA/vHwuBc7SWq9val6FEGJPY1qNvQw5xobl1VR+uwXHAcMwMEzIKg5Q2DlM+85ZiVqucFhquYQQQojGNPUqeRYwSms9Qyl1H/Ca1nqxUqoM+Bnw2I42oJTyAX/x0q8A5iilpmmtFyQluxV4UWv9qFJqf9xgqYfWejIw2dvOQd7+53vrPApcCfzXS38S8C9gHPCu1voPSqlx3vTYJh6vEELsNayQDyuUVssVc4hUxVj15UbK521I1HIFcizyOgUp6himXUmI/KIgeflSyyWEEEJA04OrUiAeBG3BrVkCd4CLiU3cxmHAIq31EgCl1BTg9KTtgjv+VZ73OR9Y1cB2zgVe8LbREcjTWs/ypv8OnIEbXJ0ODPHWeQb4AAmuhBCiSUxfY7VcNhu/r6Fy0VZwcPtzmQbZ7f0UdnZHLCwoClJVZVO1NQK4L0uOM+o/pnw2vYkmpZVBOYQQQmSopgZXy4FO3s9FwInAPOAIoLqJ2+gMlCdNrwAGpaW5A3hbKXUNkA38tIHtnI0bOMW3uSJtm529z6Va6+8BtNbfK6VKmphPIYQQjbBCJlYoAA28DPn7rzazYt5GDBM2btrEt3nfugEY7pOzeHzkNFdmjNSgKz5hGN7O0qaNpPXi8x3D8JIaiWWJj4aBY6RsGnADz+Q8pOwzkTZ5e/WBY2JNs4H1AdPcNh8YRlKe6hPH06b8DkgKUNPWW12xlc2VP5CbHyCc5SOUZZGV4ycry8KyJGAVQojm0NTg6lXclwb/F7fP1AtKqStwA5l7m7gNo4F56dfYc4GntdZ/VEodATyrlDpQa20DKKUGAVVa6692YptNVltbS1lZ2a6u3qxWLq8jGo1RWbm2rbMikkSjESmTDCNlkkEsElcVv98hYlW16O4c2/Y+NLI8Pt9JTeM0kN5Im9dQmobmJe8/fbGRmO9sk7Yp22tsntPI/B2tF41EWbfwO4h5O/eCMMcBX9DAyoJArkko10c41yCY5SMQNAkGIRgyCQQkAGsJNTU1GXPvIVxSJplpdymXpr5EeHzS55eVUuXAUcC3Wus3mrivFUDXpOkubNvs7zLcPlNorWcppUJAMVDhLT8Hr0lg0ja7NLLN1Uqpjl6tVcekbTQqGAzSp0+fJh5Oy7KMDSy2yigubtfWWRFJKivXSplkGCmTzCTlknm2VyaxOptoxCZWZxP7wWbjCjcqS9Q2OmD6HXfY/zyL7MIAOYX+RM1XKMtyf4Z90mxzJ5WVlWXMvYdwSZlkpkwql3nz5jW6bIfBlVLKDzwH3Ky1XgygtZ4NzN7JfMwBeiulegIrcQOlkWlpluPWkD2tlOoDhIA1Xj5MYAQwOJ7YC5w2K6UO9/JzIfCQt3gacBHwB+/nazuZXyGEEGKv4AuY+AKm2yC/EXbUIVoXY2tlLRtX1WLXxtwF8dFOHMBnEMi1COVZZOX7yS0KkJMfIBT2Ec62CHtBmAyAIoTYU+0wuNJaR5RSJwDjd5R2B9uJKqXGAG/hDrP+lNb6a6XUncBcrfU04EbgcaXU9bin6Yu11vFGDYOBFfEBMZKMpn4o9n95/8ANql5USl2GG7SN+DH5F0IIIfZmpmUQsCzIajyNE3OI1dnUbIywdU0dP9RtwomR6PPmeP8Hsi2CeRZZBX63FizPIivbnxKA+QPyCk0hxO6nqX2uXgGGA/f9mJ1prafjDpeePG9C0ucFuM0NG1r3A+DwBubPBQ5sYP5a3FowIYQQQrQCw2dghX1Y4e0ERrZDtM4hUh1j3YYIa77dgh2rb4bo4P5nhUyC+RbhfD/ZBQFyCwOEs/2Es3xkeUFYKCTvXRNCZJadGS3wVqXUMcBcYGvyQq31/c2dMSGEEELsgUwDK2RghUzIbTyZHXGI1MXY+H0N65dWEYsk9QPzWiGalkGowO0HllXgJ6cwQHaun3DYIpwt/cCEEK2vqcHVxcB6oK/3L5kDSHAlhBBCiGZj+g2Cfmv7/cC8ZojJ/cAcxx2O3rG9YMxnEMj2ESrwk5XvJ6coQK7XDyyUZZGVLf3AhBDNp6mjBfZs6YwIIYQQQuwM02dghn34t9MM0Yk5xCL1/cBW123GjjpgemNx2IABVpaPUK5FdlGA7Hw/OQV+srL9KQGY9AMTQuyINFYWQgghxB7L8BlYPh9WaPv9wGIRh2idzbqlVayJ2G4AllYL5guZBHMtwgVuP7CcQj/ZOQHpByaESGjSGUAp9eftLddaX9s82RFCCCGEaGWmgS9o4AuakNN4sng/sM0/1LBhWRV2xHGbIXovBHMcb1TFXItQvkVOUYCcAq8fmPc+sOxs6QcmxJ6sqY9XDkqb9gP7eet/2qw5EkIIIYTIQDvTD6x6fR2bf6gjVhfDsAHTjcAcLxoL5vgI5fnZULWFiu9W4LMMTJ+Bz2e47x3zGfgsA8syMU13mWEa+EwD0wTTZ3o/DQzDXW6a7vrx5b6kdL54egnqhGhRTe1zdVz6PKVUCHgS+Ki5MyWEEEIIsTvamX5gtVujbK2IUVG9BccBbNv7CbbjYDhubRhQP069Ub8dI/4CZyNpoTedGNDDW1K/kheQWQaGF8wZPgPTC+5My8TwUR/sWab7029g+kwsy8D0ez8tA39S8IcBls/E8PYRn5/8Mz34iweGPjMeXErwJ3Zvu9wwWGtdo5T6Pe5Lgf/afFkSQgghhNhz1fcDg2Ctj+ziQOvt3HawvQDOsd1mjY7j4DgO0YgDtbYbmDleuhheGsC23WHwbXBw3G3EAz4vxksO5AwvyDN8XtCXtDAe+hmOs03wZ5jxYA8Mn+kGgZaB4fNq4qz4tIHld4M7X8DAME18PrAC3jy/gd/vS6r5c2vufGZ98GcY4LNSA8LNm6Js3FCbCPoMr7bQ5wWOEgCK7fmxvS7bs93WyWJX2LZN+dLNbKqKsW5DLX7LPXkE/CY+qc4XQgghxK4yDUwAH6RUg2WKRMDnBX82XqDnYEchVhdLBH/1QZ+XPpY8Py34s5OCP++wjcT/TkoV38aNW1ict6j+15MS/Xnrxmv8TPezmVIDCIbpBoGmCabfTDT5NHwmPsuruYvXCHqBoM+bl9wM1DCMRDBoGEaiKaiZCPq87Rok1pOAsG01dUCLG9JmGUBH4DxgenNnam9XW2ujX1tNZGWM1avXpy70GRAwMAImRsDA8BuYAbca3xcw8Pl9WH43GIsHZH6/ieUDw5AvlhBCZALHsbHjNQCO2wTMSbpZdO8d3VoC2wHbdm8Ube/tubZ3w5m4CY2vb3v3gTb127PdmoEtmyNUb93i3pj53Jstn+XenFmW4T7Rt8Dynv7LNUO0CdPAIDnwaX114Sryi8PbTePE3O8X8e9YUlAXjQC2FwTiJL7niSAwuRbQqf+uJpqBNlYTCN7MpKag29QGemkdIGmky3iNoOF9/02fG/BhkmgSGq8xjNcKxgNC0zIT68SbgyYHhFZSzV+8X2ByTWB6M1HDSG0eahgkmoXGA8HduX9gU2uurkmbtoE1wCTg7mbNkSActjj80m68N2UhxV3ziUZtonUOdsQmGnF/2nUOTsTB2Rxz31pf512BG2O6QRl+A8NvYsYDM388KDPrgzLLxAoY+P0mAcvcbf+4hRCZbWcDDCceMJDWnMkLKNzPTtINS1I6L8Ag6Wl24ibHqX86TtKNDjaJaRI3USSCGhy8yMfr7WInr1e/TiJd8nSiI03riUWibPFvaVpiw73pwm+41w+/26TKsAyIP6W3vCf2lln/9N5yA7P4jZvP8gZoML3BGbzATa4rYndn+Iyk0C8DawDTJdUINhwQOommok0NCLHdTSf3C0zv45daO5jWNzCR1p1vpMaK9f0D4006i7fSp09L/HKal7xEOEPl5AbICZq0b7/9JydxjmMTi0EkYlMXtYlGbCIRm1id22nWDcpi2HXgRGzsahtnk+0GZdEdXOT9BvjjNWX1gZkvYGIm1ZJZfjcg88ebMEoVtBAtyrZt91rnQMyxcWz32md70UbMu1Da8QDE+2l7QUj84unYjrcdJxFoOPH+GIlgwvscv/jGAw3bSZ3nBRJ1NXWs8VckBRckAhs387RJgJHC8O4E4v/MpGmT+gDD8AYOSEtnmIDPdH8aaem8F9TWr2d46dwns/F1zPg+iM/3fnr/Ek+bDe9pvjcAQCIt3rTpDUZnuDVOphFPCyZuHteuXUtBQSGxGMRiNrGYQyzmuKPbxWzsGMSiDo5tY0fdUe+cmI0T9Z7Sez+ps4lGHYh5148YO1+WPsP7Vx+w4T0tN7zALbmZVXzgBdObTh78wPSB3wvmLMuQ5vN7gfiDGdt2a3Xj5zjbCxjSz322V8tk23aD5z0nfh5z3LRVW2vZWLGhhQ+iZTffmlr0VO5tO1prk1UXbcEdNZ+mNgsMAKbWuiZtfgiwtdZ1LZE50XSGYWJZYFkmTQvH6sVsNxCri7gXzGidG5zFa8liXk2ZHXFw6myi1W5NWSTibP8b5XOfdhJwa8iMBoIyn9/A8poy+v0+ApaJ3y/NUUTrsr0Rumw7NUiJN7WKX6jjNSa2vf0gxX3qlxakeEFHapBCfa1Jcq1HUvr4dCJAiXnfuZYOTpICC8zUz4ZJfSDiLTO8EcYSgUQggpXt336AEQ8g4vNIDi687ZIcUNQHJk0OMBL/DMyk9U1j7zvPWD6TULD5X3Abv9GNRt1ALRIP1GK2F7h5AVzU++546eyo9z2JOjgxIOrg1LrrJIK2mFP/N99UhuHe3SQFbFhe/xV//WAJJIK1+po2aS7plae97fnQ9j7HkmqDGzwXxoMc77xlJ+bX/yT5PBivTY7hnvsSgU7S+c9Lm3IubInzn3des2M2dQG5tc0kdsyhrnD3iEibepZ9CZgJ3J82fxQwBDijGfMkWpnPNPEFTULBnVvPcWyiUajzaskiEZtoxG2mGI3Y2BH3XR9O1HGDsyrbfeJZt4OLpVEflBl+t3+Z6Te8f15AFvBqywJu+9943zJ5Ytn2Gn2iGH9qGL/Y7sTFub4JWPwC7V5sbduhemst65avb/BiXX8hrg9gEhfmlr5Ix20nSMELUozkIMUH+N1mVolgxKwPKDCN+gAkPt+LKEyTtGVeQGGS6PwcD2ASQyAnpfcZXvMu48c326qstCkuLvxR2xC7B8Mw3Uoob8C7nX3AtyO27bbMiHq1bdGYe96IReO1bV4wEPOuNzbYUTtR22Z7AZoTtbFrHYhSX+u2s9//FmguWVVjs3lL3bY1zd6ofvFznu24NYcN1baknxdJCmbix+ikBCpp58RYUgDTEufDhs6Dpltzuc05MP6gJnHOc8+L6ee/+PkuMbqg9+AnPiKgkZiPdx6MnyPBjJ/rTPceyEx74FJZuZbi4nbN/3sQu6xmY4Qt0Y1tnY0maWpwdRRwSwPz3wFubr7siN2JYbi1TH7/zt+ExWJ2WlDmEI26tWSxOi8oi7hBmVNrE93sQMR2L4o7qi1raMAPr3bM5/Uxs6zda8CPxmpW7KTP8Yty/PM2TSCS21in16rs4Glios9JYxfmeI1KPE1LideW+Oov1E7EIRaOplygDQP3ou2vb7JlxC/c8Qu2YSQCkPgFGaN+NKbGgpT6GhIjEaS4zbuSLtaGmbj4S98SIX4c07v5FUSdtQAAIABJREFU3ZVrzY7Em9S7gVszNpeMOTu+XnkikShb/et2/SDigYsvNYBJ1DCbSdM+0zsP1j+4MRPnxvrAJTFtJA1hbtSnqf+cei40TDfQTg5g5DyYoeItJPBa3sX/VOPzEn1QqV/gpCSp758KaQu8H7az7brp+7QTa2/zdUm04MAhWmND7s4cYNtpanCVhXuaSGez2xyqyCQ+n0nYZxIO7dx6tm0TiTpJQVl9E8Z4YGZ7tWapA37UUduEAT8MvwEB0xvsY9sBPzZviRKJbG20dsVOeoq4oyZgiX4qbdX8ARp5mlj/OfHUML7MMuuDkO3UqGzviWJ6bUq838k2tSneRdtMPHlsOACWJ4xCiF2V3KS+JcRse4fNJTdv3kxefm6DNc2m0UhtS1LgkskPBjOa7TVV9ZqoxqI2dgScqE31uigbq6vddPHLr4E7Ap+R2l3KMAz3Gp7GqE9AfCj4lDWNeIqkeY43P2l7TmK/6ftJXd9IC3ziu0gebCLlWIz6RMnXdSOeNq3JNZB4eFnfP9TwWll49wHUX/OT+7PGh4nfpll4vD+pl5fkAD9xb5HYJmyti2zze85ETQ2uvgD+P3v3HSdXXf1//DVla9ommxBCQgz1kBAQCFUUEBQQEexSviAK+rOBIhZQ5IvYEAW+FhQFEQURERtfiSCigPrFQhQUiUcBEYK0hJ5ky5TfH+czybBuYJHdubOZ9/PxyCM7996ZfCZ3Z+49n3LOocB/D9l+GHDrSP8xM9sf+BzRp3y+u58+ZP9c4BtATzrmRHdfnPZtC3wFmEz8iu4EtAG/rHuJOcDF7v4eMzsK+Axwb9r3RXc/f6RtleaUz+fpaIeO9sKzel61WqFUS/hRC8hKwyX8SEHZ6gqlx1LCj7opjIODJcptTzxDI/99dGVdvYi52mL4pwQypC+5fx9ZWfNFtCb4iNd/VlMgRnHql4iIrFshn3/G6ZLLl/cxffqEhrVpvfM0QVKlVI2YYk0wkVszIpPLQ6EjT/uEIh0TirRPLNDRXaBzYhsPLe9j001nAWtnMcSDuhv+XIzgxc88NUBYc8zQ7ax57jNtzz9l+1MDjTXHrGP72v25f9s+nq/7S5euX9MCPwb80Mw2B36etu0DvA541UhewMwKwDnAS4FlwO/N7Ap3v63usJOBy9z9y2a2gKihNc/MisDFwBHufouZ9QKDKcHGdnX/xhLg+3Wv9x13f9cI36Osx3K5PG1FaCvm6X6WCwJqCT8GByusePhRpk3riQXOdT0rzzS6IiIiIk9jXUHSYIz0rQmSYO0ozjMESZ1dBTq6CnR0FGhrz9PeUaC9o0BHRywJWFegsXTpw2w1f1oj372sR0aaiv1KM3sFEfx8Pm3+I3CQu/9khP/WzsDt7n4ngJldChwM1AdXVWJkCmAK8K/0877An9z9ltSeFUNf3My2ADbgqSNZIs9ZfcKP/r4Ckye2Z90kEZFhVWs3puUK1TKR7bVUN9Vp1epYZ5MKeUbqc8gXYr0M+SjmmcvnyBVTz3yte15kJJ5lkESqqfR0QVJXd4H2zmcfJIlkYcQ5Wd39KuCq5/BvzQbuqXu8DNhlyDGnAj81s2OBCcBL0vYtgaqZXQ3MAC519zOGPPdQYqSqfrrpa8xsD+BvwPHufg8iIiJNrlKqUilFcoVqCpAqpQrlUlqLWU03p/lcrN1MiytyeSh0FWjvKtA+sUD7hKdOddp445mUBisM9FcY7K9Q6i/HNOm+MuUS6XGV8mCZykCsX4W1yzVyOZ5yQ1xb9pFj7dqOXKFuCnOtZlW+LngrpOAtZdeTJjU0SKoF6oMVKpXq2t8JWPdI0sTiU34HFSRJKxhpnas9Adz9+mG2V939hhG8zHDfoENXAB4KXOjuZ5rZbsBFZrYwtfOFxDqrVcC1ZrbE3a+te+4hwBF1j/8X+La795vZ24i1XHs/XQP7+/tZunTpCN7K2Lv37gFKpTLLl//bIJ1kqFQa1DlpMjonzUnnhcguV04ZN8vV9HcETtVyHJOrVteODNXuVKtEQNKRo9iZ/nTnaOvK09WVo60jT7E9F4kY2iJra7GtlpgB8vkqkYPqqXmoit05ip0PUeyCkeUSykU5hQopk16kO6/9XKtbValAOWXRK5cqlAaJAG0g3ZwPVqkMQqkvalqVB4kU6YNP/X+o1q03oVpdu3CkuuYWnioRqNWS79RnvVu7LpWUBS/WtTa7sf6sDP09XPNzLRX90ONrgXsO8u05Cp1Q7MpT7IS2yXnaO/N0dEGxvUBbGxTqfgfb2mq/gzDc7yBE+bJV/UA/8AxLmLPS19fXNPeDstZ4OS8jHbk6GzhtmO2TidGmRSN4jWXAxnWP57B22l/N0cD+AO5+YypSPD0993p3Xw5gZouBHYBr0+PnA0V3X1J7oSFTB88DPv1MDezo6GD+/PkjeCtjr5h7lDuKS5UFrckoM13z0TlpTuvTeamUI0AolyuxSH4wRpEq5bXBAbm60ZtagJR68NsmFWjvLtLWnaeju0jnxCId3QW6uoq0teWjB7+zQHt7nvb2Ah2dBQpjEBQsXbq0aa5xNZVKjMaVyqkcR6nC4GAEaeVUeLg0WKFUjuQEg4MVBvrKlAYqDA5UKPVXGByIx7UERZWBKqWBcgR1/XUjb3XnKJfPpezQ1TWjgGumqtUymRZSvblCSi5QS0ley+RXSAWKn6MRf1bSSFK5NGTK50hHkqYUaesqaCRpBJrxsyLNdV6WLFmyzn0jDa4MuGWY7X9O+0bi98AWZrYJkcHvECLbYL27iUQZF5rZfKJz7SHgauADZtYNDAB7EgFfzaHAt5/SYLNZ7n5fengQ0PyhroiIjI1K9NjXptZVSmun2lVLaYpbLWtnmt9Wq8OSL+YodhVo687TNqmdzglF2ruLdHYX6J7YRrE9H4FR3Q1qq9+cjlQ+nyffHql/x0J98DY4GMFbqVQbYasL4FLwNjBQjumSKXgb7EvTJlMgVxmMeju10h/V8jDTJkk/1II3Ik12LXhbM9qWgrf+x8s8WRl42iApl6Zi1qbbtU8q0N5doDOtT1KQJNI8RhpcrQY2Av4xZPscIth5Ru5eMrN3EYFSAbjA3f9iZqcBN7n7FcAJwHlmdjzx3XJUWkP1iJmdRQRoVWCxu19Z9/KvBw4Y8k8eZ2YHEWPSDwNHjfC9iohIk6olbCiloKhSTsXGU82gXF0Nmlx9730ueu+LXYXUe98eo0jdBTonFensjFGk9o48bR0xitSRblDHqgaSjL364K3rWWaKHYla8DY4WKFUmxaZRtueMvpWqh1XZqC/bsStv8LAfU+w0SaTFCSJrCdGGlxdDZxuZge5+yMAZjYN+GTaNyKpZtXiIdtOqfv5NmD3dTz3YiId+3D7Nh1m20nASSNtm4iINE6lFAW/y+Uq1VIlrcOJ0YPa1LpclVhbU61LlpAnjSIVaOspxihSV4HOiUU6u556Y9qWpti1p5El3ZjKaFsTvD3L2ov1li5dyfz5s0exVSKSpZEGV+8DbgDuMrM/pW3bElP2DhmLhomIyPhT6isz8GSZVfeXeHzV6rXrWFi7UL5K3ShSZ572qW10dBfTOpAiXV3FNVPs2trzdQFS4TndxIqIiIy1kda5ui8ljTicKNqbI7LvfYsYaRqamEJERNZzpdVlBlaWGVydsjpUoX1SkWnzuumau4otbCPa22OaXVvdNLv29vyYJGwQERHJ2rOpc7WKyLqHmc0G3gT8BXgesYZKRETWU4OrY0Sq1Lc2kOqYXKR3Xje9G3fTO6OTqdM66J4QqQmWLl3JlvOnZthiERGRxhtxcGVmBSLr3jHAvsCfgHOB745N00REpOEqVQb7KxFIrS6vmcfXMbnI9E27mT6nm2kzOpk2vZOurhFfQkRERFrCM14ZzcyIgOpIYCVwCbAfcERKQCEiIuPRkECqloW8o6eNGZt1M2PjbqZO72RqrwIpERGRkXjaq6WZ/RJYCFwOvN7dr0/bP9iAtomIyGipVBnoKzO4skJpVZlcPgKpzqltzNh8AjPmdDFtRhdTezvo7FQgJSIi8p94pivobsA5wHnufmsD2iMiIs9VpUr/6gikyn1rR6S6etuZsfkENpjbzdTeTgVSIiIio+yZrqo7Am8BfmlmdwHfBL49xm0SEZGRqgVST5QpD1TWBFLd09uZaROZMaeLqb2dTJveQUeHAikREZGx9LRXWne/GXinmZ0AvA44GjiDKOv4cjO7r1ZUWERExtiQQKqWbKJ7ejuzFk5i+kZda0akFEiJiIg03kjrXPUBFwEXmdnmRIKL44GPm9nP3f1lY9hGEZGWUy2nNVJPlCgPVGNEihzd09uYtXASG8yZQE9vBz1T2xVIiYiINIlnfUV299uBE83sw8CBwJtHvVUiIi2kWq4ysLrM4JMRSAGQy9E9o41ZC6cwc+NupkzrYNq0DtraVVZQRESkWf3H3Z3uXgZ+lP6IiMgIVMtVBlalQGowAqlcPgKpGdtOYYPZ3fT0djB1qgIpERGR8UZzSURExsi6AqkJG7SzweY9zJjdRc+0Dqb1dlIs5jNurYiIiDxXCq5EREZBpVxlcFWZgSdLVGqBVCHHhBntzNyihxmzu+mZ1sHUaR0KpERERNZTCq5ERJ6lNYHUEyUqpQik8oUc3Rt0sOGWE5m+UTdTezvomapASkREpJUouBIReRqVcpWBJ0sMrixTKVXJESNSEzfsYJZNYvpG3fRMa2fqtA4KBQVSIiIirayhwZWZ7Q98DigA57v76UP2zwW+AfSkY05098Vp37bAV4DJQAXYyd37zOw6YBawOr3Mvu7+oJl1EEWPFwErgDe4+11j+w5FZDyrlKoMrCwx+GSZSjkFUsUckzbsZPaCyfTO6mba9A6m9LQrkBIREZF/07DgyswKwDnAS4FlwO/N7Ap3v63usJOBy9z9y2a2AFgMzDOzInAxcIS732JmvcBg3fMOd/ebhvyTRwOPuPvmZnYI8GngDWPz7kRkvIlAapDBJytUKlVy1RRIzepkzjZTmD6zi55eBVIiIiIyco0cudoZuN3d7wQws0uBg4H64KpKjEwBTAH+lX7eF/iTu98C4O4rRvDvHQycmn6+HPiimeXcvfpc3oSIjD+VwQikBlaWqVaAKuTbaoFUN9NndjF1egeTpyiQEhERkf9cI4Or2cA9dY+XAbsMOeZU4KdmdiwwAXhJ2r4lUDWzq4EZwKXufkbd875uZmXge8DHUwC15t9z95KZPQb0AstH9V2JSFMZNpBqzzNpVgcbbzeB6Rt0rhmRyucVSImIiMjoaWRwlRtm29BRpEOBC939TDPbDbjIzBYS7XwhsBOwCrjWzJa4+7XElMB7zWwSEVwdQay1Gsm/9xT9/f0sXbr0Wb2psXLv3QOUSmWWLx/JIJ00Sqk0qHOSsUqpQrUMlUrUkSr1l7nngQeopk93vg26ZhSY9LwiU3oLTJycp3sC5PP9QD99Jbj/gfgjY6evr69pvk8l6Jw0J52X5qNz0pzGy3lpZHC1DNi47vEc1k77qzka2B/A3W80s05genru9e6+HMDMFgM7ANe6+73p+CfM7BJi+uE36/69ZWnN1hTg4adrYEdHB/Pnz39Ob3K0FHOPckdxKdOn92bdFKmzfPkKnZPRUKlSLlWplKtUSlXKpQrVElQGK1TL1QiUcpAjB7n0oFKlSoxCtU3I09adp727yCOPL2eLrefSu0EnU6d3Mmlym0akmsDSpUub5vtUgs5Jc9J5aT46J82pmc7LkiVL1rmvkcHV74EtzGwT4F7gEOCwIcfcDewDXGhm84FO4CHgauADZtYNDAB7AmenoKnH3ZebWRtwIPCz9FpXAG8EbgReC/xc661ERlelXKUyWKFcrlItVagMxshSpVyNKXlJLpeDagRHVCGXh0JHnvYJRTomFGnrztM5sUhHd5HO7gKdXUXa2vK0tedp7yzQ3p6nvb1AR2fh39ZELV3ax/z5Mxv6vkVERESG07DgKq17ehcRKBWAC9z9L2Z2GnCTu18BnACcZ2bHE1P4jkoB0SNmdhYRoFWBxe5+pZlNAK5OgVWBCKzOS//k14hphbcTI1aHNOq9iowrz3UUqTONIk3poL2rQMeEIl0TixEgdURg1Naep6OzEMFSe562trxGl0RERGS909A6V6lm1eIh206p+/k2YPd1PPdiIh17/baVRB2r4Y7vA173HJssMm7EKFKVcrny9KNI+bXBUS6XA6qjNookIiIi0soaGlyJyDMYhVGkYleejjSK1N5dpHtSjCIV2/N0dMToUW0kSaNIIiIiIqNHwZXIGNAokoiIiEjrUXAlMkLVcpX+x8o8MdhHtTTMKFIVSH/l23K0dRUoduVpn9ROx4Qi7d1FuiYU6JrQplEkERERkfWQgiuRZ1ApV1n5YD+VwSpd0/Nsss00OroLdGkUSURERETqKLgSWYdKqcrKB/uolGDWtpNZuPN0Hlp+F/Pnb5h100RERESkCSm4EhmiMhgjVdVylTmLeth6x16mTusE4KHlGTdORERERJqWgiuRpDxQYeUD/ZDLMXfHHrZe1MuUno6smyUiIiIi44SCK2l5pb4KKx/sJ1/MsenuvczfbhqTJrVn3SwRERERGWcUXEnLKq0us/KhAQrtObbYczoLnj+N7gltWTdLRERERMYpBVfScgZWlVj90CCFrjzz99mArbadSmenPgoiIiIi8tzojlJaRv/KEn0PDVCcVGTr/WdiW/fQ0aGPgIiIiIiMDt1Zynqv/4kSqx8epGNykee/YhZbbNVDW3sh62aJiIiIyHpGwZWst/oeG6T/kUE6e9tZdPAsNrMeikUV9xURERGRsaHgStY7qx8ZYOCxMt0bdrDTazdgk82nUCgoqBIRERGRsaXgStYbq5YPMLCyzKRZnex4wEZsPG8i+byCKhERERFpDAVXMr5VqqxcMUhpZYkp87rZ5eAZzJ47QUGViIiIiDRcQ4MrM9sf+BxQAM5399OH7J8LfAPoScec6O6L075tga8Ak4EKsBOQB74LbAaUgf919xPT8UcBnwHuTS//RXc/fyzfnzROtVxl5UMDlPoq9G4+gW12n85GcyZm3SwRERERaWEN6943swJwDvAyYAFwqJktGHLYycBl7r49cAjwpfTcInAx8DZ33xrYCxhMz/msu28FbA/sbmYvq3u977j7dumPAqv1QLVc5cn7+njsntVM26Sbvd80j/3eME+BlYiIiIhkrpEjVzsDt7v7nQBmdilwMHBb3TFVYmQKYArwr/TzvsCf3P0WAHdfkbavAn6Rtg2Y2R+AOWP5JiQblXKVlQ/0UylVmblgEgt3nc4GM7uzbpaIiIiIyBqNDK5mA/fUPV4G7DLkmFOBn5rZscAE4CVp+5ZA1cyuBmYAl7r7GfVPNLMe4BXEtMOa15jZHsDfgOPdvf7f/zf9/f0sXbr0Wb2psXLv3QOUSmWWL1/xzAevxyqlCgOPVKiUYeqWbWw6v4PJU1ay4uGVrHi48e3p6+trmt8RCTonzUnnpfnonDQnnZfmo3PSnMbLeWlkcJUbZlt1yONDgQvd/Uwz2w24yMwWEu18IbHOahVwrZktcfdrYc20wW8Dn6+NjAH/C3zb3fvN7G3EWq69n66BHR0dzJ8//z98e6OrmHuUO4pLmT69N+umZKIyWOXJB/qhWmXzPXpYuFMvPVM7s24WS5cubZrfEQk6J81J56X56Jw0J52X5qNz0pya6bwsWbJknfsaGVwtAzauezyHtdP+ao4G9gdw9xvNrBOYnp57vbsvBzCzxcAOwLXpeV8F/u7u/1N7obqpgwDnAZ8evbciY6XcX2Hlg/3k8jnm7TyVBYt6mTy5PetmiYiIiIg8o0YGV78HtjCzTYgMfocAhw055m5gH+BCM5sPdAIPAVcDHzCzbmAA2BM4G8DMPk6szzqm/oXMbJa735ceHgQ0/zhiCyv1lVn14AC5Yo7NXtjLgu2mMWGigioRERERGT8aFly5e8nM3kUESgXgAnf/i5mdBtzk7lcAJwDnmdnxxJTBo9y9CjxiZmcRAVoVWOzuV5rZHODDwF+BP5gZrE25fpyZHQSUgIeBoxr1XmXkBldHUFXoyLHlXtOZv10vXV0qvyYiIiIi409D72JTzarFQ7adUvfzbcDu63juxUQ69vptyxh+LRfufhJw0nNssoyR/pUl+lYMUuzKs2C/mdjWPXR2KqgSERERkfFLd7PSUP0rS/QtH6R9UpFt9p/JFgt66OjQr6GIiIiIjH+6q5WG6H+ixOqHB+mcUmS7V2zIFvOnUiw2rIa1iIiIiMiYU3AlY6rvsQH6HynROb2dnV69EZtuMYVCQUGViIiIiKx/FFzJmFj1yACDj5Xo3rCTnV83k3mbKagSERERkfWbgisZPZUqqx4eZHBlmUmzO9n55bOZ87wJ5PMKqkRERERk/afgSp67SpWVKwYprSwxZZNutn3lDDbaWEGViIiIiLQWBVfyH6uWq6x8qJ9Sf5XezSew7e4zmDV7QtbNEhERERHJhIIredYq5SorH+ynMlBlg/kTWbjbDGZu2J11s0REREREMqXgSkasUqqy8sE+KiWYtc0kFu4yg+kzurJuloiIiIhIU1BwJc+oMljlyQf7oVxl9vZTWLjzdKZO68y6WSIiIiIiTUXBlaxTeaDCygf6IZ9j7qIetl7Uy5SejqybJSIiIiLSlBRcyb8p9VVY+WA/+WKOTXabxoIdepk0qT3rZomIiIiINDUFV7JGqa/MygcHyLfl2GLP6Sx4/jS6J7Rl3SwRERERkXFBwZUwuLrMqgcHKHTl2WrvGWy17TS6uvSrISIiIiLybOgOuoX1ryzR99AAbRMLbL3/TGzrHjo69CshIiIiIvKf0J10C+p/osTqhwfpmFxk2wNnseX8HtraC1k3S0RERERkXGtocGVm+wOfAwrA+e5++pD9c4FvAD3pmBPdfXHaty3wFWAyUAF2cvc+M1sEXAh0AYuBd7t71cymAd8B5gF3Aa9390fG+j02s77HBul7ZJCu3nYWHTyLzayHYjGfdbNERERERNYLDbuzNrMCcA7wMmABcKiZLRhy2MnAZe6+PXAI8KX03CJwMfA2d98a2AsYTM/5MvBWYIv0Z/+0/UTgWnffArg2PW5Jqx8Z4NG7VlFoy7Pza2dz0Fs2x7aepsBKRERERGQUNXLkamfgdne/E8DMLgUOBm6rO6ZKjEwBTAH+lX7eF/iTu98C4O4r0mvMAia7+43p8TeBVwI/Sa+9V3r+N4DrgA+OwftqWqseHmDg8RITN+pi0f6zmLvpJPJ5BVQiIiIiImOhkcHVbOCeusfLgF2GHHMq8FMzOxaYALwkbd8SqJrZ1cAM4FJ3PyO95rIhrzk7/TzT3e8DcPf7zGyDZ2pgf38/S5cufVZvaqzce/cApVKZ5ctXPKvnVSsVBh6vUl5VoWvDAvNe0MX0DfpYPfgv3MeosS2kr6+vaX5HJOicNCedl+ajc9KcdF6aj85Jcxov56WRwVVumG3VIY8PBS509zPNbDfgIjNbSLTzhcBOwCrgWjNbAjw+gtccsY6ODubPn/+fPn1UFXOPckdxKdOn947sCZUqTy4fpLyqzEzrZpvdZzB744lj28gWtHTp0qb5HZGgc9KcdF6aj85Jc9J5aT46J82pmc7LkiVL1rmvkcHVMmDjusdzWDvtr+Zo0popd7/RzDqB6em517v7cgAzWwzsQKzDmrOO13zAzGalUatZwIOj/H6aQrVcZeWD/ZT6K8zYahLb7DadDTeakHWzRERERERaTiODq98DW5jZJsC9RMKKw4YcczewD3Chmc0HOoGHgKuBD5hZNzAA7AmcnQKnJ8xsV+C3wJHAF9JrXQG8ETg9/f2jsXxzjVZJQVVloMrMrSexcNfpbDCzO+tmiYiIiIi0rIYFV+5eMrN3EYFSAbjA3f9iZqcBN7n7FcAJwHlmdjwxve8od68Cj5jZWUSAVgUWu/uV6aXfztpU7D9JfyCCqsvM7GgiaHtdI97nWKuUqjz5QB/VMszadjLb7jqDab2dWTdLRERERKTlNbTOVapZtXjItlPqfr4N2H0dz72YmAY4dPtNwMJhtq8gRsHWC5XBGKmqVqrM2aGHhTv10jNVQZWIiIiISLNoaHAlz165v8KTD/aTy+d43o49bL3jdCZPbs+6WSIiIiIiMoSCqyZWXllh1YoBNtu9l623n8aEiQqqRERERESalYKrJjW1t4O5e3ax935b0D2hLevmiIiIiIjIM8hn3QAZ3vQZXWw2v0uBlYiIiIjIOKHgSkREREREZBQouBIRERERERkFCq5ERERERERGgYIrERERERGRUaDgSkREREREZBQouBIRERERERkFCq5ERERERERGgYIrERERERGRUZCrVqtZt6FpLFmy5CHgn1m3Q0REREREmtbzFi1aNGO4HQquRERERERERoGmBYqIiIiIiIwCBVciIiIiIiKjQMGViIiIiIjIKFBwJSIiIiIiMgoUXImIiIiIiIwCBVciIiIiIiKjQMGViIiIiIjIKFBwJfIsmVku/a3Pj4iMe7XvNGk+us6IPL1mvCdTEeEmZ2Z5d69k3Q6R8cDMNgW63f3Wum05d9cXnYiMG2Y2CXhS313NSfdm8nSaJsqT4bl7xcwKZlbIui0CZraFmb3DzL5nZoenbbn6vyVTXwBebWYzaxt0c5ItM5s4zLam62lsRWY2wcxeWjsPOi/ZM7MuM3srcBnwUzM7aMj+vK412TGzdoh7s/RYn5WMmdnBZnaVmc1KjzM/Jxq5alJmVgQ+CXzR3e9O2/JAzt3LmTauRZlZG/BzYApwJ7AI2Be4Hehw9yfTcerRyoCZ7Q98G9jK3R8wsx2AdwKdwLXA1e5+r0ayGsfM9gA+A3weuMrdV9T+/82szd0HM25iSzOzCwHc/ah17Nd3WYOZ2SeI68qdQBtQdffXpO8+hSleAAAgAElEQVSzFe7+z0wb2OLM7LPAMuBKd/971u0RMLM/ANsBn3L3D2fdHlBw1bTM7CTgE0AZuBo42d1vTvtyQN7dy2bWAzymm8WxZ2anAS8FXg0MAl8C7gYWALsCvwLe4e7LMmtkCzOz7wF3u/vxZvZG4H3AI8CTwEuAJcAhujlpHDP7OvBGYBWwghhZ/AowCfg0cKy7P5pdC1uXmXUQn4193f0XZvY84GDgRcBdRMeePisNlEZFHgYOdvdrzcyAc4GVwObAlsDlxHVmeXYtbU1mtj1xHfkF8ARxzb/W3f9oZm8Gvg88rg6JxkkjuxcAHyQ68S4BPuDuj2TZOZT50Jms077A/wDHAJOBP5jZr8xsb3evpsBqZ+BbQHeWDW0hRwCfcff70oXtcSLQ+jNwJLAJcLGmbDReGlW8n+iMADiV+KI90N0PAGYDHcB/Z9LA1vVp4DvAbsBFwEeAvwLXAHMUWGXqFOBPKbDahLiJP4n4DL0cuN3MjgFNeW6g44A/uvu16fEDwJ7ENeYtRPC7F3F/II33MLAUeBBYTXQcfczMzgbOB7ZQYNVwpwFfcvevAScDBwJvh7VTN7Og4KoJmdnmRC/vLe7+DeD1xE38Y8A1Znarmb2G+CLewN1XZtfa1mBmLyb+//+aHheA1xA9JB909x8D5wATgQ0za2iLStPLbgZ2SPOulwA3uvvjafrZQ8B5wOZmtkGWbW0V6TPyd6Cf6Gk/GZgJfA0wYGczO9vMtsuwma3s/UTgC/Bx4mZxT3c/BNgDuBB4p5l1amZEw2wM/MLMOtPjDwM3EDNXfklMS/8NsEABb+OlkdyTiKD3MOADxBTBI4iA65VpDWN7dq1sHWa2GzAfOBvA3c8GPgt8xMw+bWZd6biGxzoKrpqQu98OnAHcmB7f7+4/JEZH9gduIUasDiN6s2Ts3UQMOz+cHi8CLgZ+UHfMb4jRkWJjmybJNcAc4EpgR6LHtxZ4AdwLzHD3B7NpXmtx93JaH3oysKeZ7evufcSUwD8AJwCvBX6YYTNbkpltCVSB95vZpcDuwCfd/W8AaWT++0CBCISlMc4Evp0+JwAOnJhmquRTR+rDwEQFvI2XbtJvALYHXufuPwHeTazD/h2wDzH1+fmZNbK1nAicn6YAFgHc/Uxine+bgcPTtoaPYCm4alLu/rvaha7WQ+XuK9z9GuBtRA/WdbV1WDK23P0J4Bp3vz8tyP8dcMKQ5CKHAI+6+z3ZtLK1uftdxHQmByYAnzCzD5nZhmZ2BLGG8TtP8xIyytJnZRkxJ/5lafPRwBnufi4xlVZTnBrM3f/m7h3E6NUuQIkYuaqfAngH0EOsy5IGSMmr/lr3+Hx3/036uWJms4FXAd/IqIktzd0raSrz+cR0NIiRkt+4+0FEZ/dF7v77rNrYYi4gpprj7qXaRnc/hThHZ5vZ+7MYSVRCiyaTekZ6gC53v7due47IFFgxsw2JDHW1nhPJQP1iSTPbheiBPzIFwJIRM9uauJHfjxhhnAz8E/hf4L2aEz+20nTALnd/Mv1cBeYS0zJrKfJ3ruudl4yZ2QLgntSJVNt2OvAid989u5a1DjMr1HfW1WXVrP09C/gosa7nxdm1VADM7MtERsdTgDe5++UZN0l4yudmAvApYv3Vru6+pJHtUHDVRNJaq3cS0/1uJKYD/HXIMTliSPpId39P41vZWsxsGjFl5k3Av4hexT8Dv671lFgUrn0rMC+tV5AGMbNeIlnCDsBf3P17dfs2BKYRU5sG3N2zaWVrMbN3EaUJzhyy/RjiYnesu1+aSeMEM3sF8HN3X2lm7e4+MMwxryXWkB7q7j9veCNbVH0m4GH2HUosC/h8o28UJbJrunt/3eP9iA67JcBL0udJpQsapNZx93T/32nt4ieA9zf6vCi4aiJmdg2RcvXXRIB1G/BeYB4wC/iZr62lVKwfBpWxYWaXAdsQU2Q2IDIzPgb8HrjU3X+TbvA3Bu539/sza2yLSXOsLyUW399OzHs/z93/Z5hjC8PdsMjoSlkbazcgHwVOBwbrRnh3Bm5191UZNbGlmdnLiXOy/bquH2mE5FXAdHc/bbhjZPSkWQ9HAWfXlgKk7UNHsiYB05Qev7HMbBvifmwzYuR9MXChRy3FvYBVaZmANEj9/W/dspnqkGMyDXQVXDWJVCDwZ8C27r7MzDYCvksUEdyYGDX5GXCasgM2RjonvySGlP+ctj2f+KLdj6hz8S53vyW7VrYuMzuVmP73JuJcvJnIoLmXu/9ZHRCNlwqgHkSsbXsH8D53vyTbVkmNmd1CdNKdkDqFdicy0d4HfM/db0rHTQRKmro59szsF0QH0T3EjJWz62/WUw99sX7URBojrdX5E5EJ8J/EusQDgKnAV4GT9BlprNSp+iXgemCxuz9St+8pAVWWnapKaNE8DgB+S2Q0g0gvuTOR9eSFwDeJoqgvzaR1rWkPIqvZbbBmLu8t7v5BInnFAPDD1NMrjXcE8Fl3v83d73H3jxIZm14PscDVzOaa2RfTDYqMvXcTUzA+TmTS/KqZHWdmhfRH6aMzkkZItgQ+lDZ9hpj6tzFRVuI3ZvZRAHd/UjeNYy8tBZhJzFD5HDAD+IGZ/djM9oXIugkcb2YXZ9fSlvVBIqHLPu5+BPH9tguRCOZg4OY0Gi+NcwJR//UdwLlmdkxK9LImK2C61kzMcraKgqvm8UfiwrdPGoY+A/iKu3/X3e9w988RqXGV4rNx/o9IQ1zLcoaZdaTekL8S66wGga0zal/LShe0FcSIbn0di8uAA1LPO0QmoT00JXDsmdkJwDJ3vypt+iBwCXEj8mKP1OyaKpGdU4Dfunu/mR1OrFU8AtjP3bcEjgeOS9cfaYwtiVHD33jU6Hk3MZ22ClxgZjeY2VHAu4BbM2tl69qYKLQ9CODuq1OisXOJEd97gPdlUUephb2MqGt1GVFX9P8B55jZe8xss3TMAuA2M+vJqI0KrprIn4FHiV+YrwAV4CFYMy0AYu2V0uI2zl+J0cTzzOx17l519/7ajbq730GkMJ6bZSNb1ANEvZHaFNnaTftVxAXxBSnAOoKYLihj733AWbBmesaTwHuIqbWXm9lhtX3ZNbE1pcxZmwCbpSxn/02sT7yubursYuJmcWFGzWw57r6Y6In/S3r8F3f/KhHongjcTUyByrv76Zk1tHX9BjjMzHas35hSst9MBFnbAFtl0bhWY2ZziM4ITwMOhxKj72WiptUXzOxE4H/SMY9m1VatuWoyZvY6okhwbZHrvkQq6QOJX5hZw2V3krGRbgS/QNTmqRV3vpIIdF9AZD+bpnPSWGl6mdWyadbSr6afv0PMkX8IeK27b5tdS1uDmXUQ05d/Xnce8ql0xExifcKWRMri32TY1JZWNwqyEXEurq7bVyCSKX3J3b+ZTQtbW/33WHq8JbEO69PufkZ2LWtNKdvct4DZxHfYzzxqkdX2zyOWDuzi7n/PpJEtpm4KYH2ponbiHvnVxOyurYHt3P1PmTQSBVeZGvpFOmTf5kRP4kyil34AuMDdz2pgE1tabTFk6vV9EfBfRJHabmA5cQP/5dTTKBmrO18vIopsziOmPKnuWMbMbCpwMRGAbe1RWFgaIAVNk4cs/N4VeCiNvte27UOsk5umRDDZqU/HbmYvI87JRJ2TbKRRqw8RN+1/AH5FJLkoESOMM1214BqqruOuAGvWJdb2/QRod/d9MmsgCq4yZ2ZbEbWtHidSfP/W3a9P+yYRw54LgK8TKYy1diQjZjaZmOM7n8gW9DPgMa0jaRxbW3fszUTyl+Hqjm1ArJdb4e67ZNXWVpFuBnuJz8Zqd3+gbl+eKH5eNrPtgf9y9xMyampLsnXUHRtyzAuJdQzXu/v7Gta4FmVR860DuLz+8zLMca8GNk5ToKRBzOwA4JYhoyOHEbOJZhJlP+YSo1qfyXKEpJWY2WR3f3yY7TkgRywJ+AfwsvpR+SwouMqQmR0LvJFII91JzHVfSawluaBuYbg0iJntTZyLX7r7EyM4fp2jjzL67BnqjhGdE1WLQqn3uvsfMmtsizCztwFvIzKdfR94b20B+DDHKj1+A9nwdccGqCtUm445kJiC/oGRfO/Jfy6lkq5NI78HOB+4xN3vSBkCJ3ldMXRprHQP8Gnis/CLYfYvJO4RHgf+sa7vOhk9ZjYXeB0xc2gW0bG9GPijp9qiKcCaBpzg7h9a12s1ioKrDJnZcuJG5Jvp8YeImj13EuusjnP332fYxJZjZiuBLuLD+2WiJ/fhIcdMAfqVqrixRlh37J3qRWwcM1tEXOQ+CfQRox8vIxLybAw8AlyVAt5Mizq2opHWHTOzLqCQkpDIGKl1xpnZmcRn5A7gNKBWu+co4BPu/uX647Nqbysys98DN3jUgptLFNT+L+K+7Dvu/v1MG9iCzOwqYrbQzURCi9cSmZyvAT7p7r/KsHnDUnCVETPbj6gzsgtQdveBlAnlO8DHiSxbc4C9n27agIweM3sV8DHiRvEwovbYH4iEFlfX9ZCcCtzt7hdk1NSWZGbvIerx7JWmmdUnsdiKyBq0KbC7u/8rw6a2DDO7Avinux+bHn+ECHS3Bf5OjJqc5e6XZ9fK1mVmTxJJXa4ys3OImRIfIj4rFQDdvDeeme0BnEeMGD5ELMT/FDH6+23gTGJampYBNFBa634t8CJ3v9vMrgF6iPqJ2xBrRr9CdFTk1Fk09sxsO6JTdfMhU873ID4zuxJr375AFNtuipFEpcTNzgNAG7BzXaa5PYB57v4TYq3VdGCLjNrXijYkgqmfuvuBxDTN24hpG9dZFEN9CVEvRjVHGm+kdccWZNS+lpJGcGcR2cxqDiC+27Yjimw+CHwqJbSQBhpB3bGqAqtsuPsNwIXAscDjqaNuBfBjIq33TUTNK2msIpGsaoKZvZYYfX+Vu7/T3fcgps6+nqidqMCqMRYA/yTOTe2an3P3G1IikQ8BxxH3zk0RWIGCqyz9A1gFfN7MDjGzDwBfJEZOIOZk3wwsyqh9rejnwGXuvhzA3W9z9yOJ+jBXE2sWfkqsx/pdds1sWX8lehBVdyxj6eL2GNHJcIiZ7WpmbyFG4t/n7nemjIAfJdYmzMuutS1LdceaUFobAjFL5QXARql3fi5wjLsvIkayfpBRE1tW6qR7CNifuJZcB9xvZu0pM92viNpXe2bWyNZzAzGieyBAuuZXU5p8iM9RH3HOmoa+VDOSbkxeThQP/CpR7PRcdz83HdIO7ECk/JQG8PBjWHsBTDcly9z93cTIIsDJWbWxlaUsQQcRNx0XmdmtZnakmfWa2aKUIGYukfJbxlDdiMdPiKkyPwReTATAPXWHTiXOiUZ6GyjVHTu8ViYipS3Ou/sqYgrN9cBHzGxX9cA3XA7A3e8kOvROJ6YCXuLuD6Z9P3T3f2TXxNZTF/ReSHQKnUjco0129wF3L6d11j1EEiUZY6kTbxkxjflsM/t6So1Pbc27u99FStKTWUOHoTVXTSBla5pWm0+aUkkfDxzs7pri1ADpi3W2D6m/M2RdzyeBo919ZhZtbEXDLehOJQp2R3XHmkJdHbhriCDrRnf/pJntRtykeG1NljRO7WZxuKl/qjvWHMysm/jMbA/s6e63ZdwkAczsDcD/I0aonMgeeBfwBmLd72xlPW2c1Fn0ZmItfBexXOMK4G5iYOIwot5Y05wTBVcNltYpvJZYTHxTLevZkGN2Iz7A/+up5pWMnfRFehhRq+da4FP1mQDTdIACMT/+L0qR31hmNg84mph3fVmtzoXqjmXPzLrcfXXd4yOJnt/lxPq3PwGHpJF6yUCtBkxthMrWFuBU3bEGMbOJxEyUQ4nr/tfq9r2AWC/yb1kcJRvpM7MbMdVsL6KAcBuRGfVid/9hdq1rHUNLd6TstK8iPku7AJOAq4hzclk2rRyegqsGMrMtieHNbYje9tXAG1Mmp6f00JvZVHd/JKOmtow01/37xDqER4BXEtnOVgLm7tfWHTvB3Vdm0tAWZWZvJBarTk1/Hgbe4O43reN4pS4eY2a2MTH/fT+iTs89RBKYm9P+zYiF348DV7r7o1m1tRWlzJlvIBWff7rOINUdawwz+wLwEuBJImHFzUSnw71P+0RpiNTRcCDRwfpdd/913b6N0o+dwF2aRjv20jrQA4hO762IpEm/Aq5z9/vMbDbR4d1B1Bpruu8wBVcNZGY/Im44Purut5vZV4BF7r7jkOMKSsHaGGZ2JXCfux+THp9HjIbsQQS/JeDdnnG171ZlZvcCnwAuJ+a5/xi4w93fVrsxNLN2oNKMX7DrIzP7HfAoUW/k+UTa9aXE4u/Pu7tn17rWZmZbA18nps7cTQS5n3L3UzJtWAtLa0SuBl5BrD2cB3wXONPdv2pmHe7en77HBtU51FhmdgwxBXA68Deixui73H3JMMeqM6IBzOz9wJHAb4nvsbcTAxI3ABe4+w/qjm3KDtWmWgC2Pku9vS8kLnS3p82fBuaY2SF1x+0KaJpGA5jZNOJCV1+vansiuDqOWNNzF/HBlgZLo1aPAue5+4Pu3k9kP3uNmc2ru8gdTZNlClpfmdnbic/Hoe7+RuLz8lMi0NoZ+O+6LE7SeJ8F/gi8xN1fTmQMPCxdf9ZI6+SkMY4HfuDu/+fuj3sUOT8feBtE9rN03GeIOn3SWJ8kCjgvIq77FeCjZlYws2L9gQqsGuZ9wEnufoy7n0aUJVhGlP74Xkpe1bSBFSi4aqS9iNoVK2obUragbwOvrUuHex4xj1TGXplIu/p2M5trZvsQc3k/6O7fc/ffABcBzzMzy7KhLWoR8Ov6DR414P5OLGKtBcjnEMksZOy9GPieu68ws0npwnYjsej7/cTUp9OybGCrSlNlng98oZYcyd0/R1xz6jvw9kPnqCFS8p0Z/HvW38uBGWa2bzruYODYVE5CGsTMjgDuBy5y94fTqPuRxGj8glowZWZn1koXyNgysxcR31k3m1kx3RtfTizb2Bd4F3HPtmmzBlag4KqRfk30iBRgTZIEiExBOwCdZrY7sCXw8Uxa2GLSIvtLgK2JNVfHE0WE76877H5iusCdDW9gC0sLin8FdHoqDFiXKvcK1o5UfRD4o6vuWKP8hcjUiLs/kbYdQyR6uQ74HLB76vXNDf8SMkZ2IqbQlOEp15jLgEPrOvA+S7oOyZgbIL6vnjLikdKs/5FIXAXw38QIijTWQmL9WyesWZJxB/E995q0rZe4N/hnVo1sMX8jvp/2cvdSWuP2JmC+uz9M3DP3EAktmlbxmQ+R0eDud5rZAR7Fz3LuXk4Xu18RBdAOJip/X1w3TUDGWJrz/n+AEYHVFcArzezbRAKF9xFZG5um8ncrSD1Sl6V1imsynKXdlwLvNrMdiPSsR2XTypa0BPigmV1OdEjsQ9Tt+XLafwPwOmCOu+tmpLFuIrKdPgZQt273h8RU80VpXc8WqDh9Q6S1VF9jbcBbnx7/QmIa7d7ESMmuWbWzFaVzcR2wvUeB7frPzE+ITqNTic/OH+qTXMiYWk7Uf/ucmR1ILA04hLRcxt3/ZWbXEYkumpZGrhqoNoRZP5SZPswXAZ8nsqOcmE3rWpe735qmAf6DmJb5KWLB8Q3AFODDWbavldU6GurSSBc9igb+khgN/pe7X5ldC1tDuinHo8j2/sTn4hRi+sbhdd9pLwCKCqwaL9Wq+pi7/6u2LXXk3UFMSzuA6Cy6xN0HMmpmy0j1K3H31e4+UFsfkjpY24kkF4NECYkv6Jw0VvrOuh74GsS1pW73t4DZZnYQ8FZiZFEaIN0Tn0Tch00gZha9t1a+INXo25+4P2tayhbYBMxsAZFF6GJ3PzLr9rQ6M9ucyB60DLhK2c8aK9WCex0xlWaJD18L7q3AuURa9u82uIktx8xuAM4ekqWpvf6GMNXnuwQ42d2/lUEzW1KaAbGIKNb8+JB97enG/lXE+t4CsKG7rxjmpWSUpCmZpxDrEX+XpjMNd9z5xOh7r0qvNFYt2B2mllItC+05xH3Abe6+bXYtbQ0W9SwnE//fpRTs5tx9sJZBO92bvQfYzd2bevRdI1dNwKMq+yzgvVm3RcDdb3f397v75xRYNVaqBXc5se7w88A1ZrZ/2rdmDY+7fxV4pQKrsZcKN+5GXU9hmpK5Tfq71uu7CXChAquG+wBwBjCztsHMOgDqgt+biRpx31Jg1RBHAx8hZqKcZmYHmtmGEFlQ69a/fQDYW4FVY5nZLsDnzezXwP+Y2bG177K6QOsaYsrzyRk1s9V8lcjWOA3WnId8+rk2XbOPyEx7bBYNfDY0ciUiTUO14JqPmf0MWObuR6WaPe8g1rk9BNwG/MTdz0jHdrn76swa24LMbDnwHne/OPXsvhWYTSzSv8Tdv5eOWwjckxL5yBgyswOIdYhXAHsS5Qt+AvQTpT1mr2s0S8aWRcHgHxFZZ5cSo77dxFqfa4kZRHenTI8vd/dLM2tsi0jXlZ8D27j7P9MsiBOJhDBPEBlqx9X0fwVXItIUUi2em4EXpdFczGxT4P+Im8dL07ZdgT1qN/QydsxsE+AOoMfdHzezXxAJE84BniSmNB0OvEUjVo2Xpvud7u6WRkZqmen+AbQDC4Bz3P1LGTazJZnZJ4Hb3f0CM3sbUKsLdycxMv9H4K/NnE56fWRmi4kp/8e5e1/a9mIiBfuLiOvNm9R51zhpCuYMd3+9mb0B+BAxQnUvMatrCrHu6rcZNvNZ0bRAEWkWe6FacM3m1envD5nZccBGwDvd/Rp3v9Hd30LcjLwwsxa2thXAPenn/0dM/dvP3Q8nZTolpqWpOG2D1E1fvhw4xszmuPu5xPmoEp0TnyZGtqZm08rWlIpnTwJudfe+WhILd/+Fu7+JKOz8cqJYvTTOUmJUF6Jg8HfcfX93P5qYArga+FJtuvN4oOBKRJqFasE1nx8Qa0d2IurwXEcq2FyXXetnwCZ1wa80zt3Admb2FqKH96e1+mMpY+OniZo987NrYsuppVv/A1Gz5/Np+2eAc919N+AtwA2aGtg4KYHFSuA3wBvNbEpKnFCoW6P4M+BMYNuUWEka407gRWa2DzFadWNtR8p2eiKx3mpONs179nQxFJGmkEapDkh1LNZVC+59qBZcw7j7ne7+CeAI4v/+alJB1LqF33sAf66rQyYNksoSnEpMz9wYeJWZzag7pEDU8Hv8354sY2LI5+BEIJ9GfRcBF6RjrnL3U7JoX6uqm375I2AusNjMtnf38pDryS3A5sS0Z2mMq4iA6mxgO+DINMpYM4WozzduSnxozZWINK1a8WAzO4nIpjmZKFD7UMZNa0n16ddTrZ49idGtee6+PNPGtZi6VNITgY8RiRLagcuI0d52IvDdWamkx56ZbUUU1b4q9bbXtp8EfAL4prsflbYpIU+GUuKXLwN7E7WuziJGeHcnpgb+2d3fnl0LW8eQ77EzgdcDXUT2wJ8RxYIPJsqyHJddS58dBVci0vRUC675pCmanwV+7e7vy7o9rc7MNgPeSSROeAToAX5MFKhdkmXbWoGZXQ1sQ0ydvQm41t1vMbNeYtT3vDQ6L03AzOYQnUOHE0HxKmK06lrg2Nr0WmmctBRgN+AwotZlP3FevkMk7lmZYfOeFQVXIjIumNlMoKwRkuZhZpOJczJuLnrjnZnNJnrcfwncPdx0zFTH5x5ghabQjr20/vAsotf9t0TNt/uIKWivAnD3l6Zjc8oQ2FhmtgGwH/G5ubou82yOSHCRJ9b13ufuSzNraAtZ1zkZcsy2wL/G4zVfwZWIiMg4YWY/IKbJ/IyYAng98M+6gsG149rcfTCDJrakNBJyOlEYeEtiHdx2xLSm7wFfAH6vc9J4ZnYlEfA+DLwA+D5wlLtrXVVGhjkn3wPeBKyEp6yRG5eU0EJERGQcSLWstiXqwKwkMtFdArzDzLYxs8503MEonXTDpNGoZUTK6E+6+3Vp+vJtwKNEgoTPEZk3pYHM7J1EspfXuPsLibIRi4Ad0/5adlqlxW+QdZyTHYEdU1CVS8f1ZNfK50bBlYiIyPgwH/grMY3mVUSgdSuR0OIy4P1pLdzZxLoraYC6XvYPAAvM7KD0+EBiBOuNRIF0z6B5re5oYr3b0pQg6f+I0d4TAFJW2inAGWY2LcuGtpBnOieVdE4+M17PiYIrERGR8eEm4ItEfSvc/fZU/HQT4ErguPT3TFQLrqFSBsBHgK8Be5jZ+4FlwM/d/TZ3f4u7fyvbVrYWM9sSGARuh6ekyb8A2DHtB/gwsJfqjo299H9eAu6A9fecKLgSEREZB9z9CXf/ibuvgChVkG7ql6eMjZsQN5OfH7oGS8ZWXWr1HwEvIQo4n+Xuq9J5ymXXupZ1H5H9r6N+o7vfQAS++6WSEm8lOiZk7N1PnJN2WJNUZL07J0poISIiMo7V3bjvAfwCmKlacNlJNa9eCZzr7o9m3R5Zq1ZjzMxOJRKOXA2c5O5zs21Z6zKzoruX1qdzouBKRERkPWBmrwB2cfeTs25Lq1Oh4OYxXPr7FABfA8wGDhsuFbiMLjMz4EigDPzY3X83ZP9C4CpgI8b5OVFwJSIish5II1i54WpfibSKIbXg7hkuyDWzNiK42s7dx21WuvHCzLYGvgF0AhOBIvB8IhX7HHe/Jx13PbDQ3XuzautoUHAlIiIiIuuFddSCu2tojbFUyHaKu/+98a1sLWb2Y2A58DZ37zOzxcBPgWOIAOtvwHuJNOxz3f3PmTV2FCi4EhEREZFxL9WC+zVwHrALsB/wF+BbRCKFv6eb+1cBe7v7sZk1tkWY2VyiFMHOwD/SmrdbgFVEdtM88BbgQndfL2rBKVugiIiIiKwPRloL7kyiwLOMvX2JUcQVKbDaDtgGeIe7f9zdTwOuIGrEdTzdC40XCq5EREREZH3wbGrBfSyrRraYq4FLgb70eDrwEXf/o5kV07bfARsSNbDGPU0LFBEREZH1jpnliSQv5fR4IvAP4CGCsh0AAAhrSURBVHx3PynTxrUwM8vXJ95Ja7Dc3Y/PsFmjpvjMh4iIiIiIjC+1G/i6WnCLgF7grMwaJQBVgFQw+EXA7kSa9vWCgisRERERWW/V6lyZ2WTgkyqyna26umM7Ah8BvuzuyzNs0qjStEARERERWe+pFlzzMbNJQNndV2XdltGi4EpERERERGQUKFugiIiIiIjIKFBwJSIiIiIiMgoUXImIiIiIiIwCZQsUEZGGMLN5RI2Zndz9poybIyIiMuo0ciUiIiJjxsxONbNbs26HiEgjKLgSERF5BmbWlnUbRESk+WlaoIjIesbM9gDOABYCZeCvwNHufquZ9QJfBF4E9AJ3Ap9196/XPf86YCmwCnhTeo2PA+cCZwGHA48DH3b3i9Jz5hFT/g4H3kEUh7yL/9/e/cdcWdZxHH8/WELaSNtM0TUz049gpsBAMWYWbvYDy2zpzKXByoaW8cOCGgbF1gSNxF8spUQnbEAY/sowHyWyGbQehyL5RcMfIZQ4coISQjz98b1O3Z04z49xNsfx89oYcF/3fV3Xfd3P9tzffa/zPXBFRDzYxVwHAdcAZwA7gHZgQkT8rbSfBFwHDAPaynzHR8QjDfpbUe53J3BxOTwPmFz7bhtJBwIzylwPBdYBUyNieWk/E3gE+AwwHTgFOA+4by/j9QdmAueWvp4DpkfEotJ+HvAD4Hjg5bKGP6p8qenzwM+BDwJfAF4FrgSWl3NHA5uBy2vrWJnfOeRzOQF4Crg0Iv5UmVtPxp4HvB+4kHymcyLimkof7yGfz7nAu4AOYFJtW6ekr5A/T58D5gDHAKuBsRHxXGmfVs6tfffLmIiYX7+WZmatwJkrM7MWIukdwN3Ao8DJwKnkS++/yin9yBfk0cCJpe2nkkbVdXURsK1cfzUZ4CwD1pOB0+3APElH1l03C7ieDEh+A9wt6agGcx0ArATWAsOBs4B3A/dIqv1+WkgGF8OBwWSw889uluEi8vfbCODrwKXA+Er7bcDHgC8BJ5V7uVfSyXX9zASmksHLqr3Mvw14oPQ1BhgETATeLO1DgSXAXWWcKcB3gW/UdTWeDEiGAIvLfBYCvyLXcSVwp6R+ddddC0wmn8cG4H5JB/Vy7AnAk2XsmcAsSSMq93c/cBT58zK4zOXh8uxq+pa+x5JrfggZyAEsAn4MBDCg/FlUv5ZmZq3CmSszs9bSn3y5vTci/lKOPV1rjIiXyExEzS2SPkFmLtorx5+KiOkAkmaTL+e7ImJOOfZD8sX+dOAXlevmRsTics63gLOBcWSQUm8csCYiJtcOSLoY2EoGDKuBo8nMWu0enu3BGmwmM2adwNOSjieDntmSji33+oGIeLGcf6Oks8hA7LJKP9O7yrqRweAI4MSI+HM5tqHSPhH4bURMK/9fL+k4ct1uqJy3PCJuLvc/rVz3bETcUY7NIAOXDwPVQiAzKtm2McBGMmCc14uxH4yIG8u/b5B0BTAKeAz4OBncHRYRO8o5V0k6B/gyGUhDvktcHhFR5nItcJukPhGxQ9J2YHctG2lm1socXJmZtZCI2CppPrBcUjsZMC2JiL8CSDqADJQuIDMSfYEDgRV1XT1R6bNT0stkhqN2bJekfwDvq7vusco5eyStIjM6ezMUOKO8fNc7lgyuZpMZskvKvSytBFqN/KG29a0ypxllC98QcnvhOknVa/oCD9f1011Fw8HA5kpgVW8gmfmpehSYJql/RLxWjlXXerukN6isNfD38ndXa71d0pP8d617PXaxqTLOUOAgYEvdWvUjn0/NzlpgVenjnWSQvxUzs7cRbws0M2sxETGG3M63EvgsmbU4uzRfCUwis1ejyMzEMjLAqtpV9//OBsf25fdIHzIAOKXuz3GUzzeV7NmgMsfTgSckjd3HMTvJz3BVxxxIZoeqXu+mr7YetHc2aKse726ta+f2Zq33ZezaOH3IwK7++ZwAXFW5ZneD/v2OYWZvO85cmZm1oIhYA6wBZkp6ALiELJIwktwyWCtE0UYWPHi1SUOfRskAlb6H87/bBqs6gPOBFyKi/iX/PyLiGeAZ4HpJc4GvkkUgGjlVUlsle3UasCkiXpP0OBl4HNGoKEYvdAADJA1skL1aR6531UhgY0Rs28exIe9rA4Ckg8ltg3c0cewO4HBgT0Rs6O7kLrwJHLAP15uZ7TccXJmZtRBJx5CfHboHeImsQvcRYG45ZT1wgaSRwCvAN8kKb483aQrjJK0nt7VdRn5mam6Dc28CvgYskjQT2FLmez6ZXdtNFm1YQlYePJwMEP6vuESdI4HrJN1MFnP4NllVj4hYL2kBMF/SJDKAeC9wJrAhIu7qxb22l7kslTSBXNsPAQdHxDKykMMfJU0nC1QMK/f1vV6M0ZWpkraQ2/C+TwYxC0tbM8Z+CPg9WZTkO+Rn944APgk8FBG/62E/zwNHSxoCvAhsi4idvZiHmdl+wyl7M7PW8gaZiVpCvuzfDiwgK8FBBhmrySp3K8mtbwuaOP4UspjCGvIl/PMRsXFvJ0bEJuCjwB7g12Q58ZvIMuo7yQqHh5Z7COCX5OeMJnYzhwVkpmQVcCvwM+AnlfYxZMXAWWTAcB9ZCv6F3txoKe3+KTIAuZMsXz+HssUyIjqAL5Il1teSVRevJkuXN8MUMojqILdSjo6I15s1dsn8fZrMRN5KPoPFgMiArqeWkpUP28kA+sJeXGtmtl9p6+xstCXbzMysZyrfczWs9h1Ib9E8VgBrI6K+5HjLqHzP1WER8cpbPB0zM6tw5srMzMzMzKwJHFyZmZmZmZk1gbcFmpmZmZmZNYEzV2ZmZmZmZk3g4MrMzMzMzKwJHFyZmZmZmZk1gYMrMzMzMzOzJnBwZWZmZmZm1gQOrszMzMzMzJrg3xmRknhiAF+8AAAAAElFTkSuQmCC\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"sizes = numpy.around(numpy.exp(numpy.arange(8, 16))).astype('int')\n",
"n, m = sizes.shape[0], 20\n",
"\n",
"skl_predict, pom_predict = numpy.zeros((m, n)), numpy.zeros((m, n))\n",
"skl_fit, pom_fit = numpy.zeros((m, n)), numpy.zeros((m, n))\n",
"skl_error, pom_error = numpy.zeros((m, n)), numpy.zeros((m, n))\n",
"\n",
"for i in range(m):\n",
" for j, size in enumerate(sizes):\n",
" X, y = create_dataset(size, 5, 2)\n",
"\n",
" # bench fit times\n",
" tic = time.time()\n",
" skl = GaussianNB()\n",
" skl.fit(X, y)\n",
" skl_fit[i, j] = time.time() - tic\n",
"\n",
" tic = time.time()\n",
" pom = NaiveBayes.from_samples(NormalDistribution, X, y)\n",
" pom_fit[i, j] = time.time() - tic\n",
"\n",
" # bench predict times\n",
" tic = time.time()\n",
" skl_predictions = skl.predict(X)\n",
" skl_predict[i, j] = time.time() - tic\n",
"\n",
" tic = time.time()\n",
" pom_predictions = pom.predict(X)\n",
" pom_predict[i, j] = time.time() - tic\n",
"\n",
" # check number wrong\n",
" skl_e = (y != skl_predictions).mean()\n",
" pom_e = (y != pom_predictions).mean()\n",
"\n",
" skl_error[i, j] = min(skl_e, 1-skl_e)\n",
" pom_error[i, j] = min(pom_e, 1-pom_e)\n",
"\n",
"fit = skl_fit / pom_fit\n",
"predict = skl_predict / pom_predict\n",
"\n",
"plot(fit, predict, skl_error, pom_error, sizes, \"samples per component\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"It looks like pomegranate can be around twice as fast at fitting multivariate Gaussian Naive Bayes models than sklearn when there is more than one feature.\n",
"\n",
"Finally lets show an increasing number of dimensions with a fixed set of 10 classes and 50,000 samples per class."
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"sizes = numpy.arange(5, 101, 5).astype('int')\n",
"n, m = sizes.shape[0], 20\n",
"\n",
"skl_predict, pom_predict = numpy.zeros((m, n)), numpy.zeros((m, n))\n",
"skl_fit, pom_fit = numpy.zeros((m, n)), numpy.zeros((m, n))\n",
"skl_error, pom_error = numpy.zeros((m, n)), numpy.zeros((m, n))\n",
"\n",
"for i in range(m):\n",
" for j, size in enumerate(sizes):\n",
" X, y = create_dataset(50000, size, 2)\n",
"\n",
" # bench fit times\n",
" tic = time.time()\n",
" skl = GaussianNB()\n",
" skl.fit(X, y)\n",
" skl_fit[i, j] = time.time() - tic\n",
"\n",
" tic = time.time()\n",
" pom = NaiveBayes.from_samples(NormalDistribution, X, y)\n",
" pom_fit[i, j] = time.time() - tic\n",
"\n",
" # bench predict times\n",
" tic = time.time()\n",
" skl_predictions = skl.predict(X)\n",
" skl_predict[i, j] = time.time() - tic\n",
"\n",
" tic = time.time()\n",
" pom_predictions = pom.predict(X)\n",
" pom_predict[i, j] = time.time() - tic\n",
"\n",
" # check number wrong\n",
" skl_e = (y != skl_predictions).mean()\n",
" pom_e = (y != pom_predictions).mean()\n",
"\n",
" skl_error[i, j] = min(skl_e, 1-skl_e)\n",
" pom_error[i, j] = min(pom_e, 1-pom_e)\n",
"\n",
"fit = skl_fit / pom_fit\n",
"predict = skl_predict / pom_predict\n",
"\n",
"plot(fit, predict, skl_error, pom_error, sizes, \"dimensions\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Looks like pomegranate is consistently faster than sklearn at fitting the model but conveges to be approximately the same speed at making predictions in the high dimensional setting. Their accuracies remain identical indicating that the two are learning the same model."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Out of Core Training\n",
"\n",
"Lastly, both pomegranate and sklearn allow for out of core training by fitting on chunks of a dataset. pomegranate does this by calculating summary statistics on the dataset which are enough to allow for exact parameter updates to be done. sklearn implements this using the `model.partial_fit(X, y)` API call, whereas pomegranate uses `model.summarize(X, y)` followed by `model.from_summaries()` to update the internal parameters. \n",
"\n",
"Lets compare how long each method takes to train on 25 batches of increasing sizes and the accuracy of both methods."
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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RgyQNiPYBRwLPAq8GrnPHS1TT38bEWvsA8IDbvip2vAC8Zaz3k/EVr173hgULKAUBdmCgNnr0vR07uGXHDtri1etSTq+LFnktuABnMAwZKJXYEYZUwpBSGNYmm3nVbwJixwDyLnhqjn1tdUFV3vfJuWCqyQVSUVClYEpERERk5koaEN0DfN0Ysx44AbjLHT8Z+EMaDZOpI+f7nNLWxikuvW6fq14XBUi/qEuvi6rXpZFe53seed9nrIXDwzCkAlTCkEIQ0FupUHbBVHmUYMqjGky1ulGoKKBqccfydaNS8VEqlRAXERERmdqSBkSXUl07aBnwZmttVOjgpcAtaTRMpq45del1W9zisPXpdcal1506Qel1I/E8jyzVFLxDCabKLqDqq1TYVy5Tjo6F1bApdM8gtg/g40amMplaEBXfHhJM1Y1QTYXFdEVERERmukQBkbV2H3B5g+Nrxr1FMq14nseSfJ4lw6TX3bJjB/97gtPrxpsXBSyH8N4gNgrVW6mwp1yupfhFwVQ8kIIDwVTG84aMSEUjVNF2o/S+aITKVzAlIiIikkjidYiMMUcBFwEvAP7WWtttjDkT2GqtVdqcACOn1z0WS69bFKtel1Z63VTgex7+YQRT0UjUvnKZHhdMxUemILZ4l+cRuuNZz6vNk4rmSsVHqOpT++IjVCIiIiKzSdJ1iFYB91GdL3Qy1aIK3VQLLLyQaglukYMMl163vreX+/fsYe0UTK+bKnw3AnQoY2mV2MjUnnKZXaVSLe2vHIa1ICqaMxXGUv129fezfMcO2n2fjkyGjmyWdjc6lXcBVt4Vt1CxCREREZnuko4QXQ98xVq7xhizP3b8buBd498smYlmQ3rdVJHxPDKHGEyVfR8f2FMus7NUGpre564JqQZsbb5PRzZbDZwyGdozGVoyGfKxdD+l8ImIiMhUljQgWgX8ZYPj24Cjxq85MpsMl163vq56XTy9bn6odXrTFp+7NJLAzYXqq1TYUyox6EakYGjgBNCayVRHnFzwNCebraX05WMjTxoZFBERkYmWNCAaAI5ocPxEYMf4NUdmsyTpdQC5ffuGrCU04nZdqez67ehrTulfY+Z7Hvmoat8Ic8CiKn2DYchzg4NsDoKD1o2KtpuiND2XqteRydAWpeu5QC1aM0pERERkPCQNiO4A1hhjokVTQ2PMccC1wA/SaJjMbsOl1z20bRu59nYGgoCCe0Xb+0qlIccLQZD4eT40DqpcMYK8540aXNVvNytVDBhblb5yGDIYBOwqldg2OEgpCIh+ivHAKet5tMfS9OZonpOIiIgcoqQB0YeBtcBOoBX4OdVUuf8H/K90miZyQJReN7e5maVHH53oPUEYUqwLmsa07VLBtgUBRXdsIPYBPYloVKPFBVeJR7aGGe3Ku2pwM1XW88gmqDgYlS7fO8w8p9o6UG6eU3tsxKmjbp5TlLKn4FVERGR2Gss6RGcZY86luhirDzxmrb03zcaJHA7fjeq0ZDIN8z0PRZT+1SiQGi24irb7KxV66kazBscwNypbtz7RmLfrArOWaTiSEhWNSDrPqT8I2FsoUHL7MHSek+d5NHtedcQpm2WOC5xaM5khI06a5yQiIjLzJF6HCMBaez9wf0ptEZnyaulfvs+ccbxvJQxHHLUacAHVSIHXzlKJQmw0qxAEJA2zPKgFR7kg4Mjf/54jcjnmZbPMy2Y5wr2i7bnZ7LQIDMY6z6kUhmwfHKTLzXMKqP71Bw6e51RL1fN92rPZISNOzZrnJCIiMm2MZWHWlcA5wPM48BkBAGvtR8a5XSKzSsbzaHMFBMZL6AoZHDSCVamMOJq1s7eXIvD7gQF2l8v0N5iL5QFzMpkDwZILnuoDp3kuTW2qjz7F5zm1jnJtNM+pp1Ri++Agg3XznKJ1nTJuxKktk6mOOLm+yPs+u4KA3nKZ1kxGqXoiIiKTLOnCrB8BrgE2AdthyB+eVQdZZAryotGRMY5UbO7qYumSJbX9YhCwu1xmT7nM7nKZ3aUSe+L75TJb+/rYXS7X0tHisp7HvEyGebnckICpUQDVMo4BYVrGOs9pv1sYNz7P6blCgSe3b8fzPOZkMszPZlnggsooMG71fbIaZRIREUld0hGiK4H3W2u/lmZjRGTqyfs+Rzc1jbpAbhiG9AXB0GCpVBoSTO0qldg4MMCecrlhcYpm3x82WKoPpqZ6StpI85yCTIbF+TyBG8XbWSqxuVikHIZ4boQJoC2T4Yhslvm5HAuyWdqzWVp9n7ZMhqYp/v2LiIhMF0kDIh+4L82GiMj05rlS2O2ZDEvy+RGvrYQh+yuVarBUFzRFX7uKRZ7s62N/pdLwHu0uWKgPnobs53LMyWSm7Hwn3xVzaPZ95jY4PxgE7CuX2TE4WCu8EQVMTb7P/Gy2NrrUEQuWmn1/yqcpioiITBVJA6J/Bt4FfDLFtojILJHxvFrwQnPziNeWgoC9dcHT7ljwtKdc5mk36jTQYL6TD8wdIU2vtp3L0TbFAokm368WcWhwLqp2+PtCgd/29w8ZcfM9jyNcoLQgm2VOLBWvRSXGRUREhkgaEH0aWGuMeRx4AijFT1prLxntBsaYZuBBIO+e+31r7Zq6a94JXAdscYdusNZ+I2EbRWQGyvk+C32fhbkctLSMeO1ApTJkpGlPXfC0u1xmc7HInnKZ8jDznRoVhogHTdH5sc7NGm/Z2IhcvYpbg6urUGCjm7sUrc+keUsiIiJDJQ2IPgu8BngMOIJDK6RQBM611vYaY3LAz40xd1lrH6q77lZr7WWHcH8RmeWidacWjZKyF8132h0bcaoPnnaWSjw1MMDecrnhP3gtbr7TcKNN0fbcTGbC5ztlPI9Wt45SveHmLRGGhFTnLc1334PmLYmIyGyQNCD6a+DPrbW3HuqDrLUh0Ot2c+6lCnUiMuHi852WjnJtJQzZ1yBNL77/bLHIr3p76WuQsgfQ4eY7RUFSvlDgpN27WZrPszifbxi4pCXJvKW95XK1pLjmLYmIyCyQNCAaANYf7sOMMRlgHXAC8FVr7cMNLnuTMeYVwFPAldbazYf7XBGRQ5XxvOqITy436rVRMFE/zym+/dv+fnaWStyzZUvtfQuyWZbk8yzN51niXkvzeeZlsxMeZBzqvKVoXpjmLYmIyHTjhQ3y6Ou5dYiOAy51Iz2HxRgzD/gP4HJr7ZOx4wuAXmtt0RjzPuDPrLXnjnSvxx9/PMyPkh4zUXYFAWv372fJKJPE5dANDg7SNEr5Zzk86uP0DRSL7M1m2V6p8FwQ8Jz7ur1SoRi7rsXzONr3OSqT4Wjf5+hMhqPcnKqpFmAEYcggUHTrL1VwC9U67Z7HHN/nCN+nw/No9Txa3GhVNoXvpVAo0Kx/i1OlPk6X+jd96uPZpb+/f92qVatOa3Qu6QjRnwCvAF5vjPkNBxdVWD2WBllr9xhjHgDOA56MHd8Vu+zrwLWj3Sufz7NixYqxPD41e8tl/mvDBvwjj6wdiyYyQ/UvqLn4y/dT+SAwk9UvGirjT32cvs1dXbywQR+HYcguV/hhS7HI5mKRrmKR3xaLPDQ4WLsu53kc09R00KjS4nx+0os9NBLNWyoGAXuDgF0TMG+ps7Nzyvy/YaZSH6dL/Zs+9fHssm7dumHPJQ2IuoHbD6cRxpgjgZILhlqAV1EX8BhjFllrt7nd1UDn4Txzos3NZvnTlhbMMcdQDAKKQUAhCBgMQwpBQG+lwv5ymd5KpTqhu1xmsG7OQUg1iMrWBU45t8ijyHgJwpByg9eOSoVMsTpOEY1CeFTLV0N1PonnjnnVA/gcGA3wGlxz0Hvq763fbaDaTwtzORbmcqxsbx9yrrdSoSsWJHUVi2wsFPjFvn211DUPeF4uV5ubFA+W5mST/nM//jRvSUREprJE/4e01r5rHJ61CPiOm0fkA7dZa39ojLkaeNRaeydwhTFmNVAGeoB3jsNzJ5zvebVqV6OJyuPWXmHIQKVSDZ7c175KhX2VCiUXPEUfQqN0x/rAKavgaVYJXSBToTrHo+TKLEcBDrhgJvYXeaiOWLb4Pi2+z5xslmbfp833OTKX44R586iEIUEYEkBtuwIEVIOpIefcsdo2UAkCQqi+x703rLsmfp/ojwHVph74/Y6LRhWIfT/DbY+W2xudrwV6JAjkDjH4a3RsrNozGU5sbeXE1tYhxweDgK2DgwcFSxv6+mrBBcBct2BufI7S0nyeBbncpAek4z1vqdX3CRKkg4uIiEDyEaLDZq3dAKxscPyq2PbHgY9PVJumgpHK49Yru4ApHkANBAH7y2X6gqAWQO0ul6lEf2V1740+GjS5gCkKnnKeN+kfhuSAKJCJvsaDm+hnGP+ZRkFEs+/TGltLpsV9bctkaHI/7ybPq37wdD/34dab6czlWNHWlv43Wyd032PgvtZvj3RuyHWxACvJdiUK0uqCv4ADwVx98BcFodE9yi74i/ZLYVh7RqXuWUEYsr1SwS8WD4yCuD+iNB9CGm2T73NcczPH1eXBV1xp7fpA6b/27WN/pVK7Lu95BwVKS/J5FjU1TXi58EYOdb2l5wYGeHLHDuZnsyxssN6SRpZERCQybEBkjNkAvNJau9sY8wQjlMi21r44jcbJUFnfJ0s13340pdiIUzx46i2X6XVBVG+lQk8QEMTy+eHAh+zoQ3PtA7SCp8SiD8y1F9UPzdGHaDgw4lA/atMaG7WJgpoW36c5Cm5igU2TC2xnwoe7aBRlNvyO/XrvXpYddVQtjba7XKa7VKK7VGIwCGof6jMuzazF/bzH8nPOeB5HNzVxdFMTp3UcGHsJw5C9Lv0uHiz9pr+fn+7dW7vOBxa5eUr1wdJElgkfyUh/UCr7Pj6wbXCQZwqFIcGS7xbgjUaW5uVytCkNT0Rk1hpphOgHUCt49AO0ZtC0kvN9cr5P+yjXhW4UolgXQA3EUvb2Vyr0u9S9gINT9qLgKRqFiOY/zZQPFZX64KYuHQ0OHonzgLwbtelwAU1rJkOb+5qLBTPx4EapjrOD73l0ZLN0ZLMsyud5Yexcwf13F4327nSBUnepNOT3rNn3a6+x/N54Ls1sXjbLKXUjgQOVCltc+l08WHp0/34qsevmZ7O14Cg+X+mISSgTPhzfBZPNDUa5Ajevs6tQ4HdBUPt3LaQ6IjU/m2V+LseRbs5Sm/tvt3mKBIIiIjK+hg2IrLWfjm1/akJaIxPO87zah/FG+ftxUfBUqJvz1B8Lnnpd+l5/pTJkTkh8vkY8XS8aeZqID1EHjdrEXkNGberanPN9mt18myOy2QPBTSZDvkFQk5thAaFMrOZMhuZMhoVU1zqIlIOAPlecZZ8bUdo5OMjOUmnI6EfW/a42u3k5Y9GSyXBCSwsntLQMOV4OQ55rECjdv2cPA7HCMG2+P6SYQ/T1qKamKRXs+yOMLEVpeM8UCtj+/tq/YyHUCjwsyOVYkMsxx/07cDjV8EREZPIlmkNkjLkfeKO1dk/d8TnAf462VpDMDPHgaTRhrMxuVG2vGAT0VSr0Rql7LpAacPMvors2KlMejTpFEo/auJGsKCWw2c2v6YgtGNnqApzaiE18ro1GbWSKyPo+c32fudksi2Nrr4Wu6EA0qtRTKtVGlXaWSrV5Sj7VUcto1GQsqYnZ2DyjuDAM6XFlwuPB0mO9vdy3Z8+Q9y9uajqo8t2SKVgmfMQ0PNfXGwcG+HVfH3CgAEiz77Mgl2N+LsdCVzo8SsObCnOxRERkeEmLKpwNNFqpsZnqGkUiQ3ieR97zEn3YCcKQwVi6XhQ89cZSh3pdpb0dbjJ6zs2raHELPbbGApx8LJiJBzcTNRIlMpG82Af45wHPj43ulGL/He116Xc7SyW2l0rVuYO4kY9YetlYPrx7nlcbLTl1mDLhUZC0pVjkD4UCD9WVCT/SlQmvn6c0mWXChzNSgYeSm5u5c3CQJ1zfAkPWWVroAqb22MiS/uAiIjL5Rvw/jjHmpbHdFxtjemL7GeC1wJY0Giazh+951TShBNf+evduVhxzzKyYeC9yuHLuDwZH5HIsjR0PXKprFCxFo0m7SiUKbq5SNGrbHP2hYYx/UBipTPi2wcGDRpWeqCsTPseVCa8PlhZOgTLhjUTzNhulHg8GAXti6yzFF6XtyLc6MP8AACAASURBVGRY4NaeOsIVd2h3Ae5U/D5FRGai0f4E9ygHKt7e0+D8AHD5eDdKZDi+Kt2JHDbf82h3aV0AJ8TOxUdn95RK7HDpd7vqijpE6XctY0wrbfJ9jm1u5ti6MuFBGLKjVGJLbI7S5mHKhC+uK+awdAqVCW8kWmepXpRa3O3Kow9J+fU85mYy1RQ8VzY8GllS2XARkfE1WkB0PNWsht8DZwA7Y+cGgR3W2kqjN4qIyPSTd2mnC3K5IUFLJQyrcwBjpcJ3DA6yq1ymFAR4nkcQhkOKOoxlfpAfKxO+qmPoOMveBvOUGpUJP9qVCV+az+MViyzdvbsWRLTHXlOlAEI8tXhu3bnABUvbBwfZVChQdvPAorLh81wK3oJslrmuEl67yoaLiBySEQMia+0mtzk1/u8hIiKTIuN5zMlmq3N78nmMOx66ypNRkZTdsfS77lj6XVSKPprnN5ZRpbnuQ399mfBCEAwZUYoXdSiHIWxpnNHd5OYC1QdK7a68drTdMYnBlO95NLu5XfXqy4ZXOFAhMxMrG74wl6sFSyobLiIyvKk3a1VERKYNz/NoyWRoyWQ4EqCuqENfvCjK4CDdLg0viKWH5WIL0I4l7a3Z93lBSwsvqCsTXglDntq8mblu8dv6V19d0ZbuUolNhQK9lQr9sTLijSQNphq9xiuYSlI2fFOhwFOxsuEB1YD0iGhkKZcbEvBNlVEzkdDNrwuir/Ftt0xG2OBY/PqwwbFouxKGtdczpRImDJWKLwqIREQkHTnfZ57vMy+XA+AkN8ITuPLV+135/Xip8IG6UaV4+l3SDy0Zz6Pd9zmmrkx4EvHUwKkQTEXXJk0/HK1seMGVDf9NX9+Q1dabfZ/5LlBS2fDpLxwmgIgHCw2DiYRBSLT0RcWdK7sFjivx7TCk4t4TrfdXcSOaIdXfxyAKTtz1oduuXxMwvl/bdsVJal9jx+K/2414VP+w8OzgIK8JAlo0ejrrKSASEZEJ5Xterex0vcFYwLG7VKLbLUK7bXCwNjcmDEOa3MhUs++THce/7g5JDRyjeDBVC6pigd/hBFM5z2uYwjeWYGq0suG95TLdsbLhUUWltkyGBbEFaaP7FsOQgluEGzj4q/uQOtL5w3lv/fH4h+DDvfeQe8XORQFBdI8gdn3Iwe0J3Yf++LEgdk10zyH3dsefKRbZ0tNzYESD6u9YEAs0omNRYDJcUBHnxQOIAweHHBspoIivGxj9kcLnQJAR7eN5teOee278fU2ucmV0zqu7x0To0siQOAqIRERkymjyfea70YplsaIOQRgeCCbKZXa6D+/d5TKDQVD7AJ916XfFMKQUBGQmsDJlGsHUkNGpqKjFIQRT8SCpY4zBVH3Z8MhzAwMc/dxzIz67VuCh/gN49eTw50Y7H/+ZJvwgP2wbR3hfWHdd7fq6oClwIxXxQGjI+2OjLMMFYEFsH2B7qcTO/fvJuHX0MlQXaM7iFi53c/GaPY+MK6bh4YITfdAXGZNE/2obY86w1j4yzLm3WmtvHd9miYiIHODXFXV4YexcwQUJvZUKu93iqDvCkH2VCoMufQcOTsMhdjzreQc+eEYfPt32RARUExVM9VYq7HLBVJ8btRpJfTDVnsnQ7lLp+opF2nbtGjoawoHUKmg8ghIfCQnrAoXafoL3xO9f249dV9+G+vc0vHd9m+rmpdSPBKXuD39IdJlH9XfId1+j3+Ho9zcTO97omvi+P8r7G93Dj/23k6QNwz7H82oB30HtHuYeCgBlPCT9l/dnxpi/Az5rrQ0BjDHtwD8BbwIUEImIyKRozmRodkUdjnfHlu3YwYpFi4DqnIZyGFKKv2LHCkHAQKXCQBBQcEUJCkHA/kqFYizlqT7VKNqKPoxm6z7g1fZT/rB2uMFUvwsokwRTPaUSz7pjQRiS3bv3oJSo+H40YhFPnxqSZhVPlarbr79f/MNv/WjISG3w69oT3athKlf9fvy6Bu/zDvM9w33vvufRvWsXR8yfP2xqXLluPz5npzLMew66xu2Xw5BBN7+nPkUvnqY33P0m27AB3yjB4OLKVGi9TAVJ//W8APgW8BpjzDuAJcB3gX1U1ycSERGZkqI0o+ZRr2ysUhdARa+yO14Mgmow5V4DdV9Lbk5OJAqsopGGRgFVfMQqzb+AZzyPjmyWjkMIpjZ3dbF0yZIUWiUAm/fvZ+m8eZPdjFHFK7rVB1T1gVfD+VAN5keNKcBz+w0DxGHuET0nM8oIqcweif4FtNb+2BjzYqpB0RNU/7/yVeBj1trBFNsnIiIyqTKeR+YwqlAFdQHUkIDK/WV+wL2KbrQqCq72ufOReIWt+DyVbF0gVR9gKaVobOrT5kZKBRwuba/+mmGLHBCrpBaNQnoeOyoVMoODhC6gbo5VXEx71HEsvNgoTG6yGzNGj27aNPpFMiuM5U9C7cACYBBoAQZgSoyUioiITFm+55H3PPIAhxBYhbHgqRQLquoDqkJ8lKpSqab/uXlUjYoDxOfCRMFUfC5I1hs6v2M8jDR3p37+T63QQILgZKTWNTo3WhW1+BwXn6GBZlTcIJ5+FS96kKGaAhdtZz2vdn2U9hel0dUfi597evdujl+4kD63jteuUondpRK7ymVKsUIiUC3pHgVLWlNKZOySFlV4B9URoXuB1wMvAr5DNYXuz621Tye4RzPwIJB3z/2+tXZN3TV54GZgFbALeKu19pnE342IiMgM43keucP463sUUNUHVfH9+KhUITZa1e++xhOLogBjR6VCplg8aO2XRlXbwtjxRnM74hPy44FE/Lwfm3AfHYu/rxZkNAgw4vOXRgpCptIk/Q7f58impuqCx3UKrrpgn5vPtatcpqdUqhYVKZWA6vcQhGFt4eO879M0jsGtyEySdIToRuBKa+3X3f5PjTEvAb4GrKc6ejSaInCutbbXGJMDfm6Mucta+1Dsmr8EdltrTzDGXAhcC7w1YRtFRESkTjygajnEezQqTGF378YceeSwAUbDIEQfxsdFVEhkfu7gMLkcBPQFAf0uWNrtgqWecpmecrmWghetJ5Sfoql4IhMpaUD0UmvtU/ED1tq9wIVu9GhUrjpdr9vNuVf9H5EuAD7ltr8P3GCM8aLKdiIiIjLxGhWm6MlkOKqpabKaJMPI+j5zfZ+5DQplBGHIQGxkaZ8LknqGScXL+z55N8KUUyqezGBJiyo8NcK57yZ9mDEmA6wDTgC+aq19uO6SxcBmd9+yMWYv1XlL3UmfISIiIiIH8z2PNremVL3QlZyPUvH2x0eXSiUGSqUhwVLO82qjS02uFLrIdDX2OpuHwVpbAU41xswD/sMYc4q19snYJWOd+0ixWKSzs3M8m3lYCoXClGrPTKP+TZ/6OH3q4/Spj9OnPk7XZPevB8x3L6C6ZlcYMuBee4OAvWHItiCgr259Lp9qoYcmV0xkqqZKlkslfmstzVO0fTJxJjQgilhr9xhjHgDOA+IBURewFOgyxmSBuUDPSPfK5/OsWLEiraaOWWdn55Rqz0yj/k2f+jh96uP0qY/Tpz5O13Tq38At8BuNLu0rl4cUeiiHIT4Himvk3ZylvOdNaire9k2bONEYWg6jrL5MH+vWrRv23IQFRMaYI4GSC4ZagFdRLZoQdyfwF8AvgDcD92v+kIiIiMjU5Xse7dlswwpbUSpenwuWeiuVA0UeSiUKUVU8qgFTfVU8peLJRJjIEaJFwHfcPCIfuM1a+0NjzNXAo9baO4GbgH81xvyO6sjQhRPYPhEREREZR57n1ariLWhQFa/kAqVodClaa6mnVKK7Ul3u0qO63lQ2WtNLVfFknCVdh+gkoGKttW7/1VRHcn4NfN7NDRqRtXYDsLLB8ati2wXgLcmaLiIiIiLTWc73mef7zGtwLkrFi0aX9saq4u0olWqL88LUSsWT6SfpCNFNwFcAa4xZAtwBPABcCswBPp5K60RERERkVhotFa8QG13a74KlXaUSe8plCq4qHlRT8ZpiI0tKxZN6SQOiFcBjbvstwMPW2vONMecA30IBkYiIiIhMEM/zaMlkhi2IEKXi9QUBfS5Y2l2XihctHiySNCDKAINu+78Ba932RuCo8W6UiIiIiMihGpKKl88POVdxqXhP7NlDsyrMCdXgOIkngfcbY/6EakD0Y3d8MVo0VURERESmiYzn0ZHNcoTmGYmT9Dfho8B7qM4busVa+4Q7vhp4JIV2iYiIiIiIpC5Rypy19kG3jtAca+3u2KmvAf2ptExERERERCRlidchcqW1d9cde2a8GyQiIiIiIjJRhg2IjDF3Au+w1u5z28Oy1q4e95aJiIiIiIikbKQRol1US7dH2yIiIiIiIjPKsAGRtfZdjbZFRERERERmCtUbFBERERGRWUsBkYiIiIiIzFoKiEREREREZNZSQCQiIiIiIrOWAiIREREREZm1Ei/Maox5EfBe4AXAJdbabcaY/w5sstauT6uBIiIiIiIiaUk0QmSMeQ3wS2AxcC7Q4k69AFiTTtNERERERETSlXSE6O+AD1lr/8kYsz92/AHgb5LcwBizFLgZOBoIgH+x1n6l7pqzgTuAP7hDt1trr07YRhERERERkTFJGhCdDKxtcLwHmJ/wHmXgb6y1jxljOoB1xpifWGt/U3fdz6y1b0h4TxERERERkUOWtKjCbqrpcvVeCnQluYG1dpu19jG3vR/oHOaeIiIiIiIiEyJpQPS/geuMMUuAEMgaY14JXE81DW5MjDHHASuBhxuc/mNjzK+MMXcZY04e671FRERERESS8sIwHPUiY0wO+DZwIeBRnQPkUQ2U3mmtrSR9oDGmHfgp8Flr7e115+YAgbW21xhzPvAVa+3yke73+OOPh/l8PunjU1coFGhubp7sZsxY6t/0qY/Tpz5On/o4ferjdKl/06c+nl36+/vXrVq16rRG5xIFRBFjzPOppsn5wHpr7dNjaYgLrH4I3G2t/WKC658BTrPWdg93TWdnZ7hixYqxNCNVnZ2dTKX2zDTq3/Spj9OnPk6f+jh96uN0qX/Tpz6eXdatWzdsQJSoqIIx5irgemvt74Hfx463AP8zSSU4Y4wH3AR0DhcMGWOOBrZba0NjzBlUA69dSdooIiIiIiIyVkmrzK0BbgT66463unNJSmOfCVwEPGGMedwd+wSwDMBaeyPwZuD9xpgyMABcaK1NPoQlIiIiIiIyBkkDIo9qMYV6K6mW3h6Vtfbn7j4jXXMDcEPCNomIiIiIiByWEQMitwhr6F6/N8bEg6IM0Ex15EhERERERGTaGW2E6DKqozrfBD4J7I2dGwSesdb+IqW2iYiIiIiIpGrEgMha+x0AY8wfgP+y1pYmpFUiIiIiIiITINEcImvtT6NtVwmuqe78s+PcLhERERERkdQlLbs9B/hH4M+oC4aczHg2SkREREREZCL4Ca/7AvAS4L8DBeDPgf8JdAFvTadpIiIiIiIi6UoaEL0OuNxaezdQAda5xVU/Brw3rcaJiIiIiIikKWlANA/Y5Lb3Agvc9i+Al493o0RERERERCZC0oBoI/B8t90JXGiM8YA3knBhVhERERERkakmaUD0beDFbvsaqmlyg8B1wLXj3ywREREREZH0JS27/aXY9v3GmBOB04CnrbVPpNU4ERERERGRNCUKiOq5dYe09pCIiIiIiExriQMiY8zLgP8GPI+6VDtr7RXj3C4REREREZHUJV2Y9cPA54HfAVuBMHY6bPgmERERERGRKS7pCNEHgCustTek2RgREREREZGJlLTK3BxgbZoNERERERERmWhJA6JbgPPSbIiIiIiIiMhES5oytxn4tDHmTGADUIqftNZ+cbwbJiIiIiIikrakAdG7gV7g5e4VFwKjBkTGmKXAzcDRQAD8i7X2K3XXeMBXgPOBfuCd1trHErZRRERERERkTJIuzHr8ODyrDPyNtfYxY0wHsM4Y8xNr7W9i17wOWO5eLwP+2X0VEREREREZd0nnEB02a+22aLTHWrsf6AQW1112AXCztTa01j4EzDPGLJqoNoqIiIiIyOwyloVZXwi8GVgGNMXPWWsvGctDjTHHASuBh+tOLaY6XynS5Y5tG8v9RUREREREkki6MOvrgR8A64FVwC+BFwB54GdjeaAxpt3d64PW2n11p70Gbxlx4ddisUhnZ+dYmpCqQqEwpdoz06h/06c+Tp/6OH3q4/Spj9Ol/k2f+lgiSUeIrgY+ba39nDFmP3ARsBX4V+AXSR9mjMlRDYb+zVp7e4NLuoClsf0l7jnDyufzrFixImkTUtfZ2Tml2jPTqH/Tpz5On/o4ferj9KmP06X+TZ/6eHZZt27dsOeSziEywK1uuwS0WmsLVAOlDya6QbWC3E1A5whluu8ELjbGeMaYPwL2WmuVLiciIiIiIqlIOkK0H2h229uAE4An3fuPSHiPM6mOLD1hjHncHfsE1TlJWGtvBNZSLbn9O6plt9+V8N4iIiIiIiJjljQgehg4C/gN8CPgC8aYlwD/g4Qpc9ban9N4jlD8mhC4NGGbREREREREDkvSgOhDQLvb/hTQAbwJeMqdExERERERmXZGDYiMMVngRFyJbGttP/D+lNslIiIiIiKSulGLKlhry8DtVEeFREREREREZoykVeZ+RbWQgoiIiIiIyIyRdA7Rp6gWUlgDrAP64iettT3j3C4REREREZHUJQ2IfuS+3g6EseOe28+MZ6NEREREREQmQtKA6JxUWyEiIiIiIjIJEgVE1tqfpt0QERERERGRiZYoIDLGvGKYUyFQADZqHpGIiIiIiEw3SVPmHuDA3CHPfY3vB8aYO4GLrLV9iIiIiIiITANJA6LXA9cBn8Ut0Aq8DPg4sAYIgC8B1wCXj3MbRURERESmlVKpRFdXF4VCYbKbMms0NzezZMkScrncmN6XNCD6DPABa+19sWO/N8bsBK611q4yxlSAf0QBkYiIiIjMcl1dXXR0dHDcccfhed7ob5DDEoYhu3btoquri+OPP35M7026MOtJwJYGx7e4cwBPAEeP6ekiIiIiIjNQoVBgwYIFCoYmiOd5LFiw4JBG5JIGRL8BPmmMyUcH3PYn3DmApcBzY26BiIiIiMgMpGBoYh1qfydNmftr4P8AW4wxT1ItqPAiqnOH3uCueT7wT4fUChERERERkUmQaITIWvswcDzwSeAx4HGqo0PHW2sfcdfcbK29Lq2GioiIiIhIOrZu3crKlSupVCqJ3/Poo4/y2te+NsVWTYykI0S4ctpfS7EtIiIiIiKSsnPPPZfu7m4ymUzt2I9//GPWr19f27/oootYvXo1b3nLW2rHjDHcc889HHvssQCcdtpp3H333RPX8JQkDoiMMa8DLqWaGvdaa+1mY8y7gT/UVZ8b7v3fpJpet8Nae0qD82cDdwB/cIdut9ZenbR9IiIiIiKSzI033sjLX/7yyW7GlJAoZc4Y83bgNuBpqqlzUXHvDPCRhM/6NnDeKNf8zFp7qnspGBIRERERmQBdXV0YYyiXy3zpS1/i0Ucf5eqrr2blypVcffXVvP3tbwfgggsuYOXKlaxdu5aHH36YV7ziFbV7nHvuudx000386Z/+KatWreKDH/wgxWKxdv7rX/86Z511FmeddRb//u//jjGGTZs2Tfj3Wi9plbmPAO+x1l4JlGPHHwJOTXIDa+2DQM/YmiciIiIiIhPpyiuv5LTTTuOqq65i/fr1XHXVVfzbv/0bAHfccQfr16/n/PPPb/jeu+66i2984xvcd999WGu5/fbbAXjwwQf59re/zbe+9S1+8pOf8Mgjj0zY9zOapClzy4FfNDjeC8wZv+bwx8aYXwFbgQ9ba389jvcWEREREZkUNz/3HN/cti3VZ1yyaBEXH51sWdBLL720NofojDPO4BOf+MS4tOGiiy7iqKOOAuCcc86hs7MTqAZKb3zjG1m+fDkAl112GXfeeee4PPNwJQ2ItgIvBOrHtF4BbByntjwGHGut7TXGnA/8J9VAbETFYrHW0VNBoVCYUu2ZadS/6VMfp099nD71cfrUx+lS/6Yv7T4ulUoMDAzU9gcHBwmCILXnRc+IP3M4QRDwxS9+kT/6oz+qHduyZQsAAwMDZLNZKpVKw/sVCoXasWKxSBiGtf0gCJgzZ05tP5vNsn//fgYGBnjuuecwxtTOzZs376D7jYdSqTTmn2vSgOhfgH9wRRQAlhpj/gT4PPCpMT1xGNbafbHttcaYfzLGLLTWdo/0vnw+z4oVK8ajCeOis7NzSrVnplH/pk99nD71cfrUx+lTH6dL/Zu+tPu4s7OTlpaW2v67ly3j3cuWpfa8sfB9n3w+P6R9zc3NALS0tJDNZslkMjQ1NQ25JrouOpbP5/E8r7Zff99cLkcmk6GlpYWjjz6anp6e2rkdO3YcdL/xkMvlGv5c161bN+x7kq5D9HngduAnQBvwf4EbgRuttV89lMbWM8YcbYzx3PYZrm27xuPeIiIiIiKS3MKFC9m8efOox5I677zzuP3229m4cSMDAwN89avjEkKMi6RFFbDWfhJYCJwB/BFwpLX2b5O+3xhzC9V5SMYY02WM+UtjzPuMMe9zl7wZeNLNIfoH4EJrbZj0/iIiIiIiMj4uvvhi7r77bk4//XQ+85nPANV5Px/72Mc47bTTWLt27Zju98pXvpKLLrqIiy++mFe/+tWcemq1LltTU9O4t32sEq9DBGCt7QcePZQHWWvfNsr5G4AbDuXeIiIiIiKSzP3333/QsSVLlmCtre2vXLnyoEVX3/a2t/G2tw39SP/ggw8Oe9/LL798yP573/te3vve9wKwceNGfN/nyCOPPLRvYhwlCoiMMXngr4FzgOdRN7JkrT1j/JsmIiIiIiIzxU9+8hNe+cpXMjAwwHXXXcc555xDNjum8ZlUJG3B14E3AHcAvwGUyiYiIiIiIol973vf42Mf+xiZTIbTTz+dNWvWTHaTgOQB0WrgAmvtT9NsjIiIiIiIzEw33XTTZDehoaRFFXYAI5a/FhERERERmW6SBkSfAP7eGHNEmo0RERERERGZSElT5u4B/grYYYx5DijFT1prnz/eDRMREREREUlb0oDoZuBk4MvAdlRUQUREREREZoCkAdGrgXOttQ+n2RgREREREZGJlHQO0bNAMc2GiIiIiIjIzHP77bcPWdB15cqVbN68eRJbNFTSEaIrgc8bY/7aWvu7NBskIiIiIiLpOffcc+nu7iaTyZDNZlm5ciWf/vSnWbRo0YQ8f/369RPynKSSjhD9O3A2YI0x/caYffFXes0TEREREZHxduONN7J+/Xp+/vOfs2DBAv7u7/5usps0aZKOEF2WaitERERERGTC5fN5zjvvPP7+7/8egAceeIAvf/nLPPvss3R0dPDmN7+Zyy+/HIBiscgnP/lJfvazn1GpVDj22GP52te+xsKFC9m/fz+f+9znePDBB/E8jze+8Y1cccUVZDKZg55pjOGee+7h2GOP5WMf+xgtLS1s2bKFX/7yl5xwwgl84QtfYNmyZQBs3LiRz3zmM/z617/miCOO4AMf+ADnn3/+uPZBooDIWvudcX2qiIiIiIhMuoGBAdauXctLXvISAFpaWrj22mtZvnw5Tz31FJdccgkrVqzgVa96Ff/xH/9Bb28vDzzwAE1NTXR2dtLc3AzARz/6URYuXMg999zDwMAA733ve1m0aBEXXnjhqG340Y9+xDe+8Q1OOukkPvrRj/KlL32JL33pS/T393PJJZdwxRVX8PWvfx1rLZdccgnLly9n+fLl49YHSUeIMMbkgbcDJ1Etu/1r4BZrrYotiIiIiIiM4Oabb+ab3/xmqs+45JJLuPjiixNde+mll5LJZOjv72f+/PncdNNNALzsZS+rXXPiiSfy+te/nkceeYRXvepVZLNZ9uzZw6ZNmzjxxBM55ZRTAOju7ubBBx/k0Ucfpbm5mdbWVt75zndy6623JgqIXv3qV/PiF78YgNWrV/O5z30OqI5WLV68mDe96U0AnHzyybz2ta/l7rvvnviAyBhzEvBjYA7whDv8HuDTxpjzrLWd49YiERERERFJ1Ve/+lVe/vKXU6lUuO+++7jooov40Y9+xNatW7n++ut5+umnKZVKDA4Oct555wFwwQUX8Nxzz/GhD32Iffv2sXr1aq688kq2bt1KuVzmrLPOqt0/CILERRoWLlxY225ubqa/vx+ALVu2sGHDBk477bTa+UqlwurVq8ejC2qSjhB9BVgPXGSt3QdgjJkDfJfqYq2vHddWiYiIiIjMIBdffHHi0ZuJlMlkeM1rXsNVV13FunXruP7663nHO97BN77xDfL5PJ/97GfZvXs3ALlcjssuu4zLLruMrq4u/uqv/orjjz+eV77ylTQ1NfHQQw+RzSZOQBvVokWLOP300/nWt741bvdsJGmVuTOBT0TBEIDb/iRw1rDvEhERERGRKSsMQ+6991727dvHC17wAvr6+pg7dy75fJ4NGzbwwx/+sHbtQw89hLWWSqVCe3s72WyWTCbD8573PM4880yuueYaent7CYKAZ599lkceeeSw2nb22WfzzDPP8J//+Z+USiVKpRIbNmxg48aNh/ttD5E0hCsA8xocn+vOiYiIiIjINPG+972vVgFu8eLFXHPNNSxfvpw1a9Zw7bXXcvXVV3PGGWfwute9jn37qmMi3d3drFmzhu3bt9Pa2sr5559fS1/7/Oc/z/XXX8/5559PX18fS5cu5T3vec9htbG9vZ2bbrqJa665hmuuuYYwDDHG8PGPf/zwvvk6XhiGo15kjPkOcDrVeUMPucN/DHwNeMRa+64E9/gm8AZgh7X2lAbnPaqpeecD/cA7rbWPjXbfzs7OcMWKFaN+DxOls7OTqdSemUb9mz71cfrUx+lTH6dPfZwu9W/60u5j/Qwnx3D9vm7dunWrVq06rcFbEqfMfQB4GvgZ1RGhAvBT4Cnggwnv8W3gvBHOvw5Y7l5/Bfxz2nXz+AAAIABJREFUwvuKiIiIiIgckqTrEO0BLjDGLAdOBDzgN9ba3yV9kLX2QWPMcSNccgFws7U2BB4yxswzxiyy1m5L+gwREREREZGxGFMZCGvt08aYbW67d5zbshjYHNvvcsemTUB08803c8MNN9Da2jrZTZmx+vv71b8pUx+nT32cPvVx+tTH6VL/pi/tPl6zZg2+nzQZa2ZasGDBkJLaU9VYFmb9IPAhqkEKxpitwBeBL7tRncPlNTg26n2LxSKdnVNjGaStW7cSBEGtdrqMP/Vv+tTH6VMfp099nD71cbrUv+lLu4/DMCQIgtTuPx2USiUGBgYm/JljjQ2SLsz6earzeq4DfuEO/zFwFbAI+MiYntpYF7A0tr8E2Dram/L5/JSZsLZixQouuOCCKdOemUgTFNOnPk6f+jh96uP0qY/Tpf5N30QUVTjxxBPxvEZ/85c0hGFILpcbrqjCsO9LOkL0buDd1trvx47db4yxVCvNjUdAdCdwmTHme8DLgL2aPyQiIiIi01Emk6FUKtHU1DTZTZk1SqXSIS0MO5Z3bBjmWKLkSGPMLcDZwEJjTBewBsgBWGtvBNZSLbn9O6plt0ct5S0iIiIiMhXNmzeP7du3s3jx4lk/l2giBEHA9u3bmTt37pjfmzQguhm4lGr57bj3A/+a5AbW2reNcj50zxARERERmdYWLlxIV1cX1trJbsqs0dbWdkhFHJIGRHngz40xr+XAwqwvA44B/s0Y8w/RhdbaK8bcChERERGRGcT3fZYtWzbZzZAEkgZEJwKPue1j3dfn3Cs+a2k8qs2JiIiIiIhMiKQLs56TdkNEREREREQmmmZ4iYiIiIjIrKWASEREREREZi0vDKf3tJ9169btBDZNdjtERERERGTKOnbVqlVHNjox7QMiERERERGRQ6WUORERERERmbUUEImIiIiIyKylgEhERERERGYtBUQiIiIiIjJrKSASERERkf/f3nmHSVJVb/hdFhaQpIBkEAT5yJIkZwQEUUlKkiQLgmTJSM5RRAUJgkiSDCI555zzR1wy/GDJaUn7++PcWophZne6Z5Zmes77PDxMV92uPl1dW3XPPed8J0n6LekQJUmSJEmSJEnSb0mHKOmTSBpQ/p/XcJIkSZIkSdI0OZkcDeQkffRje3j5/xettqWdkfRDSXN02DagVfYkSU/J6/ebIZ+Do588x6OPXHTtf2Rj1tGEpIEAtj9vtS3thqQfAcsBywLn2z5d0gDbw6v/t9jEtkHSJcAdwHG2X2u1PUmSfLuRNAHwft6HRx+SBtn+pPZ6jFwcTJKekQ5RLyJpTOBA4O+2ny/bxgAGpGPUO0gaC7gWmAh4BpgPWB54Chjb9vtlXD4geoiknwH/AWax/ZqkeYEtgHGAa4ArbL+UTmjzSBq/umZr2yrnPq/hXkTSeMAiwDW2v8jz3LtIGhdYD1gVGBP4m+2LavvHAIbnvaLnSDoceBG4xPaTrbanHZH0K2BzYCPbr+R9ov1Jh6gXkbQrcADwOXAFsLvt+8u+AcAYtj+X9F3gnXwwNI6kfYno0GrAp8AxwPPAbMBCwM3AH2y/2DIj2wRJ5wHP295O0gbADsBbwPvAT4F7gLVsP9dCM/sskpYADgP+Clxue2htkj6W7U9bbGJbIelkANsbdrE/Jzw9QNIBxOLUM8BYhPOzellIGZr3id5B0jzEvfc64D3imXeN7fsk/Q44H3g3r+WeIeleYG7gINt/arU9yegncyN7l+WBvwCDgQmBeyXdLGkZ28OLM7QAcDrwnVYa2odZDzjM9iu23wDeJZyjh4D1gRmA07JOoGeUSNyrhHMPsDcxcV/Z9krA1MDYwF4tMbA92Aj4CXAcca/YARhf0lTASWXhJOkFJI0NrAv8u7z+gaStJZ0j6TBJP8gJZPNIGgRsA+xie01gV2BiSRcDZwDPSjpb0qSttLNNeBN4DPg/4CNgA2A/SUcC/wR+lNdyz5D0S2A6YBNgW0knSPpe2Zfz5jYlf9heQtJMwFDgAdv/Bn5DTNTfAa6S9LCk1YGtgclsf9A6a/smkpYmzufj5fVAYHVgJ9s7274YOBoYH5iiZYa2ASU6cT8wr6QpiRXJ22y/W6IXrwMnADNJmqyVtvZhDgHOAhYGTgX2IK7tq4BpbL/dQtvajT2BB21fJ2kG4Fhi0v458HPgKUmDIUUXmmRr4D7b15TXrwFLEgtVmwC/ApYiFg2THlAibbsS53gdYCcifW49wklaRdJyxUlNmmNf4BjbJwK7AysT6XMp5NTGpEPUS9h+CjgUuK28ftX2hUTU4mfAA0RkaB3iAZE0zt3AzsQKGUT90GnABbUxtxORizG/WdPakquAaYBLgPmJCQ61VK6XgO/b/r/WmNd3Kc78k8AwIsVzd2By4ERAwAKSjpQ0dwvNbCd2JJxPgP2JlfUlba8FLAGcDGwhaZxMZW6KaYHrJI1TXv8JuJFIG7+JqPu8HZgtHc6eUSIUNwLzAL+2fRkRnZsIuJMQG/ob8OOWGdmHkbQwMCtwJIDtI4HDgT0kHVJq5TJS1IbkD9qL2L7T9hPw5Sqj7aG2rwI2Ix4K11d1RUlj2H4PuMr2q6XW4k5g+w6CFWsBb9t+oTVWtg+2hxCr5wbGAw6QtJukKSStR9TLnTWSQyRdYPvzct3uDiwpaXnbHwMTAPcC2wNrABe20My2QNLMwHBgR0lnAosCB1b36pJ6ez4wkHBGk8Y5AvhPuYYh7hm7lDTxMUpGxJvA+Olw9gzbX5To8T+JSAbEhP12278kFlxPtX1Xq2zs4+wC/NP2W0UoC9tHEPWevyNSbzNS1IakQ9QLSBpD0sSSpq62VRLQtVWE8YiVyMNaYmSbUN2Eag/Vz6p9khYk8qn37eStSRMUBaP9ifSuuwhhhReJmqJryHPdNMWpfxE4CVixbN4YONT2sUQ9XKYY9RDbT9gem4gSLUjcMz6Cr6THPQ18lxAMSRqkqKo+Xnv9T9u3l7+/KM/GVSk1XEnPsX0qEZXbEdgQOKpsf8j2Aa20rY9zEpG+jO0R8wvbexJO6JGSdsyUxPYjVeZ6SKkd2oJIhbuNWBV7vMOYAUR4e33b237zVvZtJE1MrOpuBLxMPHgfAm6pbliSfghsCkxf0mCSJpA0CVHTMi/wiO3zavumACYmVtI/se3WWNl3Kaly49p+v/w9nCjePYFImQNYoLbSnvQykmYDXigR52rbwcDithdtnWV9E0kD61H6jj3hSg3iPkSx/9Kts7TvI2ls28Nqr1cA/kfUeP7U9gepltj71K7l8YCDiHqihWzf02LTkl4kHaIeIukq4APgFsIpehT4IzA9MCVwtb/sjTNmfcUh6R6SzgbmJFZxJyMU+t4hIhZn2r69TOSnBV61/WrLjO3DlPSAM4lI5lNETvoJtv/SydivTIKS7iFpS6Jf1hEdtg8mHrRb2T6zJca1IZJ+AVxbJopfaWZZG7MGIcaytu1rv3Ej24B6W4lO9q1N1NH+NSeQzSFpTmJ+MSOxcHIpcLKjP9xSwIclhTzpAdUi1cgcylIndwCwYzqe7UU6RD2g9Fe4GpjL9otFLvccogfDtEQ042pg31SVa45yjm8iVmMeKtt+TDwcViD6MGxp+4HWWdkeSNqbSN3aiDivvyPUo5ay/VA69D2jSJlXq7v7AAcDn1YP1SLJ/7DtD1tkYlsh6efEOZ6nq+u2RC9WBSa1nemfDVBSlDcEjqzqscr2jhGjCYCJnX2ImqKkZj1IKMg9R6R7rgR8Dzge2DUjyj2n/nyr1YAP7zAmo29tTCpx9YyVgDsItS0IZZIFiMn6vYRU45+JVLosjm6OJYhz+SiMCF0/ADwg6V/Eyu6Fkhax/UoL7WwH1iNSPh8tr/eRtBAhIf+Q7c8kTUfIvG6TEaKG2Rt4hBCi+APwpO0zqp25wtvrHAhcWa7bSYi029WAV4DzbN/t6EB/CrVaxKTbHEzcn1eUdBvhGN1Z3RfKavuYJTXxvZEcJxk5OxO1bcva/rSonO1DSJnvQJz/9fP+0TwlO+IYSTcAl9p+q7ZvhBNU6uEyO6JNSVGFnnEfMDOwbAlpHwocZ/sc20/bPopQL0r5y+a5lVB+qorOkTR2uSk9TtQNfQrM3iL72oISnRhKRDXrkqJnAytJGr+83gNYIh8ITbENkWaxPyEVf7yiOejA8l/KEfcSJXoxM7Bb2XQYsXgyLdG77HZJ+wDYfj9X2Buj1M5OTqSHHwV8H7hA0sWSlodQUgS2k3Ra6yxtC6Ylemh9CmD7I9svEb20VgNeAHZIGegesT0wmFioOlbS4EokqxbBHyhp/Hz2tS/5D6hnPAS8TUwajwO+AF6HEatjELVEqVzUPI8TUbgTJP3a9nDbw6qbku2nidXd6VppZBvwGtHbokrtrFIFLiceyIsUp2g9IpUuaQBJ2wMv2r68bNoZOINQPlvaIcOd+cu9x57AHbaHSVqXEApZD1jB9szAdsDWZSEraZyZiUjb7Y4+LdsQUYvhwEmSbpS0IbAl8HDLrGwPbgfWkTR/fWOR376fcIzmBGZphXFtwopE36GzicbuvweOlrStpBnLmNmARyV9t0U2JqOZrCHqBST9mmi8WuVULw9MSKTM/QWYsrNi3qR7lJWvvxGSxFUD3EsIZ3MRohh94jzHzVOiE6oUEitVnfL3WUT++uvAGrbnap2lfRNJrwB72T6+SsGQ9B1CxnUlojnrGZmj3nOKEtRdRE+ni4lGlcfa/nNtzIxElO4g2/9piaF9HEXT4Kcq0aCybSZgIUJEYTWiJ9xULTKxLShF/KcDUxM1Q1cXmfNq//REWvmCjjYJSQNImoaIIF9X7s8TEtfuL4iF1teJxcLlgC9sL9cyY5PRSjpEDVKfKHaybyZC/WVyYsX9E+Ck+oM4aYwqX7dMchYHfks0C/0O8AYxUf+H7eNbaGZbUjv3ixP9Q6YnVtivaq1lfQtJYwOLEWpnlZNZOUWTE5OcmYGNXHq3JD2nFqGYiji3V9T2DSSUQY+xfUprLGwfOj4XFc1wbwMOsX1o6yxrD0p0aDci/f5e4GZCaOEzIto5eUrGN08tPe6l2rZBxKL2asR5nx2Y2/aDLTEyGe2kQ9QEkmYheg+9S8g/32H7hrJvAmBtIrz6L0I1KnNOe4myejM+IWDxPULF751MN2oOfdnj6XeEOEhnPZ4mI2q5htpesFW2tiuSvgecRjhNszuatSZNUBydCTsURS8EvF7Sa6ttyxIRoolTObF3qEtvS1qROL/j5/ltDkkrAQ90mKSvQ2ShTE60RZiOiB4dlhP1nlFbpBoII2rgqn2XAYNsL9syA5PRTjpEDSJpK2ADQjVnHGAOou7iRiIadPlI3p50A0nLEOf2JteaJ45kfJdRu2TkaBQ9nghnf7iin8tLtu9tmbF9kDJJnIRw4j+y/Vpt3xjAgDKBnAf4re3tW2RqW6Au+jx1GLMYUS9wg+0dvjHj2gBFv6yxgXPr13In41YDpi3CQkmDlGfgIcBOtq/rZP8cxDPyXeDZSnAhaRxJE9p+t5PtA4ABRA3ts8CK9Shz0n6kQ9Qgkt4A/lilWUjajejb8gxRN7S17btaaGKfR9IHwLhE9OcfxMTlzQ5jJgKGpTpU86h7PZ62yJXH5pG0GbAZocJ1PnHv6HTyouzz1CPUeZ+nT6g1DC1jVibqPHfqzoJLEhRp4qpO8wWi/u0M208XZbkJbJ/XMgPbCEl3ATfa3r60OliVSBd/BjjL9vktNbANKOf110QK/pTEfONS4D6X5u7FKZoY2N72bl0dK2kPUmWuASStQMgSn1PySwFOIepY/kKs1pxc6gKSJpC0KrEa81vi4XsecKWkDSRNURu6HTFxT5qn0x5PtncG1iLO/38VDYeTBpE0HzEx/xewLyEKsoikxSWtI2nFSmq7pGukM9Qz9ib6PO1JqEStXlQpR6S+FGf0ckL+PJ2hblLuDZ8RkbUjCCGbrYC7JO0PnEREmEeMb4mhbUCpRZ6MkDMHOJF4Ht5JTNzPlfQPSQNSartHHE/02HuS6A23NHARoZK4GERjVttD0xnqH2Rj1sZ4DRgLWKCqGSImldPbvkzSHcBjwI/K2KRxpiAm6VcW1a3ZgF2I1cinJR1DTOD3JNSMkua5lSjUXZFQ46oEAD6z/bikTYHLiHq4l1tmZd9lL+DsKm2o1GIdAMxFPISHAeMR6UepLNdztiFUEC+XNCXR52lSov9Q1VhxuO2PWmlkX6SWkvxf4AQiynYmUXB+EBEBXaw8Ax/IutkeMSYhGDSepDWIlK2fVrWFkn5KTODPrM1DkgYoComLAjPVUj/3lrQEcT3fIGk7Qt12zExJ7B/k6kJjPAt8CPxV0lqSdgL+DuxX9n8C3A/M1yL72oFriUnkGwC2H7W9PjADcAWx4n4lUV+Unbl7xuPEqmP2eOplSkrnlITSVsVKxELJ3ESX+f8DDiqiCkkP0Kj7PA3POsOeY/tG4GQiOvSu7ZOIhs4XE31w7iYc06RJSuuD1wnp8s+A64FXJQ0qBf83E72JlmyZkX2f2YDnKEEBRbP3AbZvLGp9uwFbE4vd6Qz1E9IhagDb7xD5po8Q4db1iP4Wx5Yhg4B5CTnMpAkcVNGKejrRi7a3ISJyALu3ysZ2oRSS/pJQgzpV0sOS1pc0iaT5ioDIdIQCWtJNyoP1HaIh5VqSFpK0CdGnbAfbz5TV3n2INNvpW2dt27AD8GcYcb94H9iWqJE7t6hzVUIWSRPU0uDOIvq/TVVW2qcDBtuej4gYXdAiE/s8tXN8MnF/2IWYc0xo+xNHA+ePge8S4jdJc9xIRDVXBigLgcMVPZ8grvGPCac06SekqEKTlOLciatwa0mH2Q74le3ZWmpcH6U8DKbuKDusrzYJPRDY2HbWaTVBZ4p8RSp+UbLHU68i6TdEF/lPiMjn3MC6tu8r+5chHrxT5Spk85Q0z0VtX1vbln2eehnVmgZLOpTo7zQfEa3ftKXGtSGS1iRq4ZYETKjODQHWBFYnnpVZd9gg1TNQ0p6Ew3kWcLTtuzuMuxc40fbRrbAz+eZJh6gblPSXNYg89LsrRa4OYxYmblL/y7zexik3/3UIieJriA7yH9f2DwQGEqkaj6S8efMoOptvTKQMnF1Jjip7PPU6+rKh8FXAhcBttg8s94t9iKDoVq20sR2oVtY7u1aVfZ56HUnfIa7neYAlbT/aYpPajnJNL0xEKZYimoOORSihnWb7wtZZ1/cpCym/I+Yd4xK1yRcBzxPZP+sQDW/T6ewnpEM0ChQdt48merV8B/gI2KAU7nbszv091xoCJt2jpF2cT6S3vAWsQsg+fwDI9jW1sePZ/qAlhrYBkjYgcqO/V/57E1iz4+pYbXz2eGoSSePWC/glrU+kwrwBfEqk1q5V0uuSXqDqHVKLZFSRouzz1ASSxifSwNcmFgNPrO1bhKixOKNV9rUT5RpdmVgUPMf2LbV9ldLnOMCQFGFpno7tDYoa6KrEdb4gMAGhRHma7bNbY2XSCtIhGgWS/kvk+e9j+ylJxwHz2Z6/w7iBqazTHJIuAV6xPbi8PoGIVCxBOKCfAds4m6L1GEkvEUpn5xI56BcDT9verHpQFEn5L3JlrHEkTUtMalYgerW8QCgm3l/2z0j0wHkXuMT2262ytR2QNAuRQjQb8K+RRY47ToSSUSPpb8BPgfcJ0YT7CSf+pZYa1mYoGt7+HpgUeILoabil7Xs6GZvXcROU+sGViMjPLITgzc3A9bZfkTQ1kYUyNtHsNs9xPyMLTEdCmdwsRqRvPVU2HwJMI2mt2riFgFx5bAJJExNF5SfVNs9DOERbE3UtQ4DNv2nb2o0SHXobOMH2/9keRhSiry5p+toDYGOymLRZziNWG98hUuUOBk6XdLQk2X7a9j9sn57OUM+QNDvRB24N4n7xP0n7djU+JziNIWl+YvK4MbAsUWc4GVFnWKUcUdTPsu9QzzgQOIaoydqaSM/fR9JARUPcEeR13DTbE5LaHxLpnqsRNZ7HS1rV9ku2n7f9JJCL2/2QdIhGzlKEjOjQaoPtZ4D/AGvUFItOIMKsSeN8TkiMbi5pOknLEqHrnW2fV4qgTwV+IEmtNLQNmA+4pb7B9mVET5z1YISDejQhqJA0gKTNiYn52rY3IBz7K4FXgAWAvWoqRknPORy4j+jR8nNCaW6dspA1glLHlTTOdsAFtm+1/a7tB4l+cJtBKHOVcYcBP2yRjX0eSesBrwKn2n7TtoH1iX5ls1UOkKQjKrXEpCl2AHa1Pdj2voQ8/ItEe4Tziqpqpon3Y9IhGjm3ECs1A2FEYT/E6sK8wDiSFiUUjPZviYV9nFI/cQYwO1FDtB3RmPXV2rBXiVSCZ75xA9uEsoJ7MzBOpWhWW9W9iC8jQjsD9zl7PDXD0sB5todKmqA8VG8jFKJ2JFKPuoxgJN2npLf8GPhbpfTpaIA7FKhH71cgz3nDFOXJ7/P1FhLnAt+XtHwZ9ytgK0fPsqQ55iBSEceBEen3TxPtPVYv2yYhno3PtcrIvoykxYl7w/2SxiyL2ecSNcvLA1sSi7I/TGeo/5IO0Ugo0aCVbL9cVg0+L/+QbiY06n9FrDqcVlstSxqkyDqvD/yRUJEbG1hF0rilmHQHQr0vpYmbxNGY8mxgExhRbF7d+M8EfihpXkJ1Z88WmdnXeYRIK8L2e2XbYEIV8XrgKGDRkgaTKUY94yeEGtTn8JXFqrOBtWvR+8MpC1pJQ3xCLJR8JT3L9rNEVG71smkvIt0raYJyH7geeNzRO4taLfJlRFoXRLrXvXWhhaQhniDuA0vZ/qyIUmwEzGr7TWKR+7uEqELSTxlz1EP6N9Wksb5qUByjU4G/EsWP07TIvLbB9sNEI8tKVOEg4mEwC5G+9afWWdc+VI57TYVrTNtDJN1ERESfsH1JK23sw9wD7CzpXCLauSwwAPhH2X8j8GtgGtu50tsz7ibk+d+Br0wiLyQmj/MVcZAfEamiSQPYHibpRL50OOuy5icT6Z/LEGldC7XKzr5O6YdzA5EV0VEw4XTiPP8S2BTYoEVmtgNvEL3gjpK0MlFLuxal9rssel9PzDeSfkpGiBqkJnf5X0Ie8yzbr7fQpLbD9l+JlfbHgL8RDRVTzrxJJE0kabCkDSXNWd9Xe/heTUTmMvWzQcrEG9sXE6mHExFRtqFEI9ZqMWURYMx0hnpO6SW0n+2Xq20liv80kea1EhFZPsP2Jy0ys0+iaDqO7Y9sf1LVVJTJ+yDgCkI2/moiZTHPb5OUc/shpU65Vi80pu2hRPT+fODlXKhqnrJgsiux0DoekaL/x0pGvvQq+xmxaJX0U1J2uwcouqB/bvuNVtuSJJ3RSR+tD4EN3XkfrV/avqhFpvZZJN0IHGn7gtq2QfWJoqIR6xnA7rZPb4GZbUFJhZuPaGj7bod9g8oEflVC+GYgMEWZWCbdoKQe7knUvt1Z0ok6G/dPIr12klysag5JCxIqqvMSaYgGbrF9b23MKhTlyrw3N46iCfmEwKOlpcSYRJ+yT6tWKZJmArYFFrad0eR+TEaIeoDt19IZSr7lHEaIUixme0Iisrk/fDUNtDwc8oHbIKWp38LUVhZLLdac5f+Uh/AMwMnpDPWYnYBDgcmrDZX8c80BvZ9oOHx6OkMNszGwB7ALsK+klSVNASHbX6vN2glYJp2h5lA0YT2H6J91H+HkDwYOk7SbpOnK0GuIKHPem5vjeELGfGIYEYEbo/xdpdl+TCiBbtUKA5NvDxkhSpI2pcgP3w8sbvvRsu2HwK3AtrbPLNsWApawfWjLjO2jSLoaeNH2hqVvyx+ADQkp+UeBy6rzKmlc2x+1zNg2QNIbxLV7WlnZ3RSYmlDoOsP2eWXcHMALRcUy6SaSViJq3i4CliRk5C8DhhG94KbuKmqUdB9JlxKSz1vb/rhsW5oQF1qcuEdv5Gz23jTlfnwtMKft50qUfhdCMOQ9QhE00xCTEWSEKEnal6XIPlqjDUkzAMsQK5AQ0biJgRWAVYCngL0lrQtRk9EKO9uFkgo3tDhDUxApiIuV3V8QEY0/QIi0pDPUOLYvJYr577M9FxGNm5dw9J8FfiZp1lRJbJ7SF2sC4GHbH1eNV21fZ3sjos/Tz4mm2UnzbARcXpyhNYkmrGMD7wJTALuVtMUkAdIhSpJ2JvtojV4qSdzdJG0NTAVsYfsq27fZ3oRY6V2syyMkjTAUeKH8/XsiLW4F2+tSpPkJpyibhDZBzck5FxgsaRrbxxLndjih6HcIEUH6Xmus7NuUus0PgNuBDSRNVGpbBtZSP68GjgDmkjRRK+3t4zxGRDYhmrCeZftntjcm0uM+Ao6pznuSpEOUJG1K9tEa7VxA1Fv8hOjFcj0hEV/VDUEocc1Qi8YlzfM8MLekTYju8ldW/Z6Kct8hRC+oWVtnYp+mkta+l+jb8tey/TDgWNsLE33Mbsy0ueao1W3+F5gOuFTSPLY/73APfgCYCXj/m7axjXgGWFzSssBLhFAIAEWNchfiOZhtUxIga4iSpF9RGrJ+IWlXohHuhERfnJSOb5LSPPiXhDN0QQexikuJxqw7tsq+dkLSlsC6RHRoQmC16tqVNCnRy+zXtm9qnZV9n5KSeCxRg3EYML/th1prVXtRauD+QaTd3kCkyFXNnTcDHrK9eess7NuURajTCYntcYmFwC1LhI7iKP0HmKrWfiLpx6RDlCT9EEmzEZPH02yv32p72oG61Hbp17IkEUWaPtUoe0YlES9pfGA/osB/EHA2kQI6CFgCWKDUviTdRNIsRBPhy8vKebV9V+AA4BTbG5ZtA7PQv/eQNA1xn1iX+A0+JKJC1wBbVRHQpDE63C+OAH5DOEXHE1H7WYgMiXtsb931kZL+RDpESdJPyT5ao49Sm3U40Vdkh1bb025ImhHYAtgAeAv4LnAx0Sj0nlba1teQdAXRp+x6QoTlGtsPSJqESKkdjOn3AAAQpUlEQVQ9oaTfJj1A0mSE4MoywBU1lc8BhMjCGERt5yu2H2uZoW1GqZ1dGFgH+DVRV/QhcBZwcBUxSpJ0iJIkSUYDkiYkHM584DaJpKmJCeRNwPO2v+hkzIKE2MLQrIVrjFLr9mdiBf0Ool/WK0SNy6oAtpcrY7/SyDlpDEmXEOf3TWAR4HyiSXbWCfUSXTmdHcbMBbycC4FJR9IhSpIkSb6VSLqASG25mkiPuwF4rtaEtRo3lu1PW2Bin6ekbR1MNFudGfgdMDeRVnQe8Dfgrjy/zSNpC0IZcU3bj0lahKhv2cj29VUqoqTvZbPb5unE6TyPkN/+AL7ajDxJOpLKR0mSJMm3jlLYPxewGzGh+SvRe+gPkuaUNE4Z9yuyZ0tTlKjPi4QE8YG2ry81hY8CbxNKZ0cRaopJ82xMpB4+VoRtbiWc++0BijM0EXCopIlbaWhfpTid0wKr216MaHcwPyEIMpyioijpu62zMvk2kw5RkiRJ8m1kVuBxIvVlVcI5epgQVTgb2LHUah1J1BElDVJbMd8JmE3SL8vrlYlI0QbA/YBbYF5bIGlm4FOiUTO1tM+TgPnLfoA/AUulpHnTjMrp/KI4nYel05l0RjpESZIkybeRu4G/E/2HsP2U7Y2IlJhLgK3L/ycnGws3TUnXegs4EVhC0o7Ai8C1th+1vYnt01trZZ/mFUI17isNQG3fSJznFYoq5abENZ00SHEqPwOehnQ6k+YYc9RDkiRJkuSbpUgOX1a9Ln1FBpRi6B0k7Q08C/yjY01R0n1qMtr/BS4nInGb2f6wnPPhWXvRPOU63q2+rSZffgkht/0Z8K7tyzo5RDJqXiWczkHwpQCI7RslVU7nEMLpXLtlVibfalJUIUmSJOkzFJliiL5D1wGTZ2Ph3qH0JFoFONb22622p53oTKWvnO+rgKmBdTpTRUuaQ9KYtj8rCydzA1cAu9qerrWWJd9W0iFKkiRJ+hySfgEsaHv3VtvSTmTz1d6hg2T8C52dU0ljEQ7R3Laz2L8JJAlYH/gcuNj2nR32z0FEPqcinc5kJKRDlCRJkvQ5SqRoQGe9iZKk1XQhGT+ko3x56Z0zke0nv3kr+zaSZgf+DYwDjE+UgfyYkN2exvYLZdwNwBy2J2mVrcm3n3SIkiRJkiRJeokiGX8LcAKwINEs9BGi99A1wJO2P5a0KrCM7a1aZmwfRtLFwBtEzdvHki4FrgQGE07RE8AfCcnt6Ww/1DJjk289qTKXJEmSJEnSe3RXMv4Iot9T0iCSpiOar+5PyJpD1GKtCZxJROZWAHa0/U46Q8moSJW5JEmSJEmS3uNrkvHARkXSfBdCXnt7YCzCSUoaZ3nC6RlaGtvODcwJzGf7PgBJkxP9tca2PayFtiZ9gHSIkiRJkiRJeomUjP9GuIJIi/u4vJ4U2MP2fZXCHHAnIbX9WYtsTPoQWUOUJEmSJEkymknJ+NGLpDHqIiulpsi2t2uhWUkfISNESZIkSZIko5mqD5GkCYED0xnqdarzOwhYHFiUkOROklGSDlGSJEmSJMk3x8XAJa02ot2oNb6dH9iDSEl8o4UmJX2ITJlLkiRJkiRJ2gZJEwCf2/6w1bYkfYN0iJIkSZIkSZIk6bdkH6IkSZIkSZIkSfot6RAlSZIkSZIkSdJvSYcoSZIkSZIkSZJ+SzpESZL0GyRNIelKSR9IankBpaQhknb4FthxvaS/NzB+KUnDJU3aw889WdLFPTnGtxFJe0t6rZyjDVttT53e+u26OPYOkoY0+J62vAaSJOlbpOx2kiT9iR2AqYC5gfe+qQ8tnenXsD1Hh10/AT74puxoRySdDExqe+VujF0d2A+YEXga+JPtCxr4rOuBJTvZ9ajt2cuYOYC9gNWA24B3uvm+2YF9gHmBGYB9bO/dXds6sXUc4A5gLuAntu9u8P0rAHsDcwDDgFuAHW0/0cAxrmcU37ubxxlYbPktMCXwCnA6sLftz7p7nCRJkq5IhyhJkralNEAcw/bbZdNMwD22n2yhWSPIxozfHJIWBs4inJXzCYflHEmL2r6jm4dZDRhUez028BBwdm3bTOX/F9YacXbnfd8BhhTb9u+mPSPjcOBFwiFqCEkzAP8F/gqsB4wPHApcypffrzt053t3h52BLYANyvvnAv5NOGr7FZunAV6q9aJJkiTpNukQJUnSVpTV5J8Sk6dVgBWBG0oqzw/KmPWBf9vesKTO/dr2ubVjDAH+bvvw8no48HtgOWAl4DVgT9un1d4zFXAY8DNgXOAJYLvymXvVjgOwke2TO/mc6YCjiv0AVwFb236x7N8bWIOYMB8ATAZcAwzuqgGhpPWAY4H5bD9eth0MrAvMZfutTt7zW2AbYBbgI+AGYFvbL3UYupCk/cu4R4BNbd9TO84iwEFEJOwt4CJgZ9vvdmZrJ3YMBI4HlgGmICb4JwCH2/6inI8Nytjq3C5t+/pODrctcJ3tA8rrAyQtXbavLUnAvcDmtk8px/xZsXkJ27fbfrODfesC4wEnldd7U35r4AtJ2B4wqvcB2L4LuKvs362L8zEA2JG4FqcCngIOqV+HZdyvgKWJa2Wlzo7FyH+7+YCxgF1tf16OeRBwraRJq2tN0k7AHwmH6XzgmfoHdOd71/btDmxV9p8D/MH2R2X3IsD/bP+vvB4i6SJgwdoh9gOWknQqcIrtp7r43kmSJF8ja4iSJGkLJM0u6VDgeSIS8AHhnNxYhvwEuJpYnZ6SmPA3wp7EqvmPy/FPklQ5WOMRTsP0wKrAnMC+5X1nAUcALp87ZdnW0f4BwIXA5IQDsDQx6b2w7KuYHlizfM7ywDyEc9Qptk8tdv9H0iBJSwHbA+t35gwVBhET+x8DKwOTAv/pZNzhxOr9/MRk+BJJ3ynfZ07gSsKh+DERLZibTibDI2EM4CXgN8CswJ+A3YCNap9/NvG7Vuf21i6OtXCxp84VxGQb2yYc2L9LmlHS94GTgQNs397FMTcBLrP9Qs2eTcrflT3deV932R/YmIiWzEY4m8dJ+nk1oERK/kE4vB91dpCarZ3+dsDdwKfAYEkDS5PLDYC7as7Qb4o9exFpfiaco5HR1fdekrhGlgVWJ67rQ2r7bwaWljRL+ezZiH8jl9bGbE38m1sMsKRbJG0q6bujsClJkiQjREmS9F0kTUJM/NYn0mguJ1b8L7I9rD7W9uuShgEf2X61iY87tVqJl7QH4VAtDjwHrENEMBauRWqertn5PvDZKD73p8SkcEbbQ8r71iGiAMsSk36I+/aGtt8pY47nSwehKzYHHgD+TkTM/mz7uq4G2647Lc9I2hx4TNI0VbSqsJ/tK4odGxERnHWAfxKRjLNsH1ENLse5T9Jktv9vFDZj+1PCEa0YImleYG3gRNvvS/oIGNaN33QKIrJX57Wyvfq84yWtSNSnDCV+w07T1yTNTEzkV6m9/31Jb5e/O7Wns/d1h+J0/xFY3vZNZfOzkhYgHKRLSkTtdOAI2/dLmn4kh+zyt7M9RNJyRKTmaMIxvY+4diq2JaKsx5XXVcSt05S6UXzvz4mo6fvAw5J2Bk6UtKvtDwjnaALgUUmfE/8GDrB9THUA2+8B/wL+JWlaot5oW+CoEk36N3C57S9Gck6SJOmnpEOUJElfZitihfpW4Ee2nxuNn/Vg9YftzyS9TqSsQURpHuwqba2bzAq8XDlD5XOekfQyEQ2oHKLnKmeo8HLNjk6x/U5RO7sOuB/YfWTji9OxFxHRmRioIlTTERPnittqn/G+pIeKrRBpVzNJWrM2vjrOjMAoHaJiy2bAYCL1cFwilavZ37ljfcmATrYNJqIdsxMphZ93caxNiOL+Sxq0odn3zQaMA1yuryokjkXUHkFEzz4F/tyN43X520maAjgROIWIDE5ARF/OlrRMcSpmJRzfjsfsqsZoZN/7weIM1Y8ziLhOHiQiousTDtsjxHV5lKRnbZ/Y8WAlAnUQcJCktYiU0d8QYhVDurAvSZJ+TDpESZL0ZY4nJoDrA49IugA4FbhmJBPZjgzny4l6xVidjPu0k/dVaccd398MnU3O65/VHTtGxuLESvzkwIREBORrlEjEFYQDth7huEwK3MRXC+RHxRjEhPnITvZ1rEXqlOJM/YVQB7wVeJeIhqzagB0Vr1KLBhUm4+tRozmAicrfUwPPdmLXICKF7IRGVM6afV+h+o1/QaSF1qmuiWWJ3/nTKIkawe2SzrK9bjc/awvgA9s71Wz/LfACkWJ4cyOG9/B7Q9TmHW77zPL6oZKuuivhuHX8vEkIJ+q3RKrsVUSE6MWOY5MkSSAdoiRJ+jC2XybqZw6QtBAx6ToTGCbpDOA02/eN4jCvU6v1kDQ5Xdd+dMW9wG/rBecd+AQYOIpjPApMLWn6WsrcD4k6okcbtOcrlLSqPYg6nt0JYYLVuhg+C+EA7Wb72fL+rsYuRCmkL47UHERUAeKczN7D4vbFgDtsj+iRJGnGDmO6c24hog7LEZPriuWo1RyVepNTiPqacYFTJf24ExGIVYhz9LXJ+Cho9n0Q18Aw4Ae2r+1izEaEKEHFVIRzuy4hm11nZL/ddwjnuU71unLMHivHqKdXLtSFXaP63nNKGq+kx1XH+YQv0067smfEQoCksYl6t/UIIYnHyvdZrckU2SRJ+hHpECVJ0haUwvfbJW1LrKJvANxZUnxuGslbrwW2kHQrMck6EPi4wY8/A9iFEEDYlViJnhN4r9TqDAF+UFLRni/bh3U4xtVEnc/pkrYmIkZ/IxyLribAo0TS+ERdybG2L5L0GFHHs3Fn6UbFvmHAlpKOJlKj9uvi8LuX1MGXiVqfT4hzAVH3cbukY4HjiL5PswC/sP37bpr/BLBhqet5CliLqEOpi0EMAVYsKnFDgXdK7VFHjgJuLL/PBUSUaWnC6ao4FnijfJcxiML9o4lJdp1NiSjkMzRGl+8rUZQq3XAcYApJcwPv237K9nuSDgcOLyIbNxLqbgsBX9g+vnJga8es0tCe7lD7BSP/7S4BtpO0V9k2AfHv4gWgUqI7CjhF0l3A9YSi3YLAV5TlRvW9C2MSIiX7Ek7cwUQ0qXKQ/gfsIulZImVuHqKe6pTaMY4hHKIzgAVs39/FZyVJknyNVJlLkqStsD3M9rm2f0GkPI0qurI9sVJ+PXAukebVrfqW2md+QEzUXyImb48QTTarVLfzCEWsa4iI1NqdHGM4sZL+erHlOiLNaxX3rLfKUcRkd6fyOU8SghBHSfpRJ3a8zpeS5Y8StURdqYftQijo3Qv8CFi5msTafhBYglDFu4Fw9g7i6ylqI+M4QkXuDEKSevryeXVOIKIBdxPnbtHODmT7VsKh2oCoS1kfWNOlB5FCnvyXwLq2Py0O6zrAGpJG/F4lardM+dxu0433TUUIF9xH1M78vvxdr9PZg2hQugNxjV1FqLJ9La2vG4zst7uW+O6/KjZcQaTl/aw25qxiywFlzJx0UrvUzfN1Q/k+1xHO6rWU67WwFfFv8xjitz6iHO9PtTEHAVPb3i6doSRJGmXA8OHZwyxJkiRJkiRJkv5JRoiSJEmSJEmSJOm3pEOUJEmSJEmSJEm/JR2iJEmSJEmSJEn6LekQJUmSJEmSJEnSb0mHKEmSJEmSJEmSfks6REmSJEmSJEmS9FvSIUqSJEmSJEmSpN+SDlGSJEmSJEmSJP2WdIiSJEmSJEmSJOm3/D9MGqGBLqYEFwAAAABJRU5ErkJggg==\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"sizes = numpy.around( numpy.exp( numpy.arange(8, 16) ) ).astype('int')\n",
"n, m = sizes.shape[0], 20\n",
"\n",
"skl_time, pom_time = numpy.zeros((m, n)), numpy.zeros((m, n))\n",
"skl_error, pom_error = numpy.zeros((m, n)), numpy.zeros((m, n))\n",
"\n",
"for i in range(m):\n",
" for j, size in enumerate(sizes):\n",
" skl = GaussianNB()\n",
" pom = NaiveBayes([IndependentComponentsDistribution([NormalDistribution(0, 1) for i in range(5)]),\n",
" IndependentComponentsDistribution([NormalDistribution(0, 1) for i in range(5)])])\n",
" \n",
" for l in range(5):\n",
" X, y = create_dataset(size, 5, 2)\n",
"\n",
" tic = time.time()\n",
" skl.partial_fit(X, y, classes=[0, 1])\n",
" skl_time[i, j] += time.time() - tic\n",
"\n",
" tic = time.time()\n",
" pom.summarize( X, y )\n",
" pom_time[i, j] += time.time() - tic\n",
"\n",
" tic = time.time()\n",
" pom.from_summaries()\n",
" pom_time[i, j] += time.time() - tic\n",
"\n",
" skl_predictions = skl.predict( X )\n",
" pom_predictions = pom.predict( X )\n",
"\n",
" skl_error[i, j] = ( y != skl_predictions ).mean()\n",
" pom_error[i, j] = ( y != pom_predictions ).mean()\n",
"\n",
"fit = skl_time / pom_time\n",
"idx = numpy.arange(fit.shape[1])\n",
"\n",
"plt.figure( figsize=(14, 4))\n",
"plt.plot( fit.mean(axis=0), c='c', label=\"Fitting\")\n",
"plt.plot( [0, fit.shape[1]], [1, 1], c='k', label=\"Baseline\" )\n",
"plt.fill_between( idx, fit.min(axis=0), fit.max(axis=0), color='c', alpha=0.3 )\n",
"\n",
"plt.xticks(idx, sizes, rotation=65, fontsize=14)\n",
"plt.xlabel('{}'.format(xlabel), fontsize=14)\n",
"plt.ylabel('pomegranate is x times faster', fontsize=14)\n",
"plt.legend(fontsize=12, loc=4)\n",
"plt.show()\n",
"\n",
"plt.figure( figsize=(14, 4))\n",
"plt.plot( 1 - skl_error.mean(axis=0), alpha=0.5, c='c', label=\"sklearn accuracy\" )\n",
"plt.plot( 1 - pom_error.mean(axis=0), alpha=0.5, c='m', label=\"pomegranate accuracy\" )\n",
"\n",
"plt.fill_between( idx, 1-skl_error.min(axis=0), 1-skl_error.max(axis=0), color='c', alpha=0.3 )\n",
"plt.fill_between( idx, 1-pom_error.min(axis=0), 1-pom_error.max(axis=0), color='m', alpha=0.3 )\n",
"\n",
"plt.xticks( idx, sizes, rotation=65, fontsize=14)\n",
"plt.xlabel('Batch Size', fontsize=14)\n",
"plt.ylabel('Accuracy', fontsize=14)\n",
"plt.legend(fontsize=14) \n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"pomegranate seems to be much faster at doing out-of-core training. The out of core API of calculating sufficient statistics using `summarize` and then updating the model parameters using `from_summaries` extends to all models in pomegranate. \n",
"\n",
"In this notebook we compared an intersection of the features that pomegranate and sklearn offer. pomegranate allows you to use Naive Bayes with any distribution or model object which has an exposed `log_probability` and `fit` method. This allows you to do things such as compare hidden Markov models to each other, or compare a hidden Markov model to a Markov Chain to see which one models the data better. \n",
"\n",
"We hope this has been useful to you! If you're interested in using pomegranate, you can get it using `pip install pomegranate` or by checking out the github repo."
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.7.3"
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pomegranate-0.13.5/binder/ 0000775 0000000 0000000 00000000000 13740675601 0015356 5 ustar 00root root 0000000 0000000 pomegranate-0.13.5/binder/requirements.txt 0000664 0000000 0000000 00000000052 13740675601 0020637 0 ustar 00root root 0000000 0000000 pomegranate
watermark
matplotlib
seaborn
pomegranate-0.13.5/dev-requirements.txt 0000664 0000000 0000000 00000000214 13740675601 0020150 0 ustar 00root root 0000000 0000000 wheel
pandas
cython >= 0.22.1
nose
numpy >= 1.8.0
scipy >= 0.17.0
sphinx >= 1.6.0
sphinx-rtd-theme >= 0.2.0, < 0.3.0
networkx >= 2.0
pyyaml
pomegranate-0.13.5/docs/ 0000775 0000000 0000000 00000000000 13740675601 0015043 5 ustar 00root root 0000000 0000000 pomegranate-0.13.5/docs/BayesianNetwork.rst 0000664 0000000 0000000 00000023301 13740675601 0020701 0 ustar 00root root 0000000 0000000 .. _bayesiannetwork:
Bayesian Networks
=================
- `IPython Notebook Tutorial `_
- `IPython Notebook Structure Learning Tutorial `_
`Bayesian networks `_ are a probabilistic model that are especially good at inference given incomplete data. Much like a hidden Markov model, they consist of a directed graphical model (though Bayesian networks must also be acyclic) and a set of probability distributions. The edges encode dependency statements between the variables, where the lack of an edge between any pair of variables indicates a conditional independence. Each node encodes a probability distribution, where root nodes encode univariate probability distributions and inner/leaf nodes encode conditional probability distributions. Bayesian networks are exceptionally flexible when doing inference, as any subset of variables can be observed, and inference done over all other variables, without needing to define these groups in advance. In fact, the set of observed variables can change from one sample to the next without needing to modify the underlying algorithm at all.
Currently, pomegranate only supports discrete Bayesian networks, meaning that the values must be categories, i.e. 'apples' and 'oranges', or 1 and 2, where 1 and 2 refer to categories, not numbers, and so 2 is not explicitly 'bigger' than 1.
Initialization
--------------
Bayesian networks can be initialized in two ways, depending on whether the underlying graphical structure is known or not: (1) the graphical structure can be built one node at a time with pre-initialized distributions set for each node, or (2) both the graphical structure and distributions can be learned directly from data. This mirrors the other models that are implemented in pomegranate. However, typically expectation maximization is used to fit the parameters of the distribution, and so initialization (such as through k-means) is typically fast whereas fitting is slow. For Bayesian networks, the opposite is the case. Fitting can be done quickly by just summing counts through the data, while initialization is hard as it requires an exponential time search through all possible DAGs to identify the optimal graph. More is discussed in the tutorials above and in the fitting section below.
Let's take a look at initializing a Bayesian network in the first manner by quickly implementing the `Monty Hall problem `_. The Monty Hall problem arose from the gameshow *Let's Make a Deal*, where a guest had to choose which one of three doors had a prize behind it. The twist was that after the guest chose, the host, originally Monty Hall, would then open one of the doors the guest did not pick and ask if the guest wanted to switch which door they had picked. Initial inspection may lead you to believe that if there are only two doors left, there is a 50-50 chance of you picking the right one, and so there is no advantage one way or the other. However, it has been proven both through simulations and analytically that there is in fact a 66% chance of getting the prize if the guest switches their door, regardless of the door they initially went with.
Our network will have three nodes, one for the guest, one for the prize, and one for the door Monty chooses to open. The door the guest initially chooses and the door the prize is behind are uniform random processes across the three doors, but the door which Monty opens is dependent on both the door the guest chooses (it cannot be the door the guest chooses), and the door the prize is behind (it cannot be the door with the prize behind it).
.. code-block:: python
from pomegranate import *
guest = DiscreteDistribution({'A': 1./3, 'B': 1./3, 'C': 1./3})
prize = DiscreteDistribution({'A': 1./3, 'B': 1./3, 'C': 1./3})
monty = ConditionalProbabilityTable(
[['A', 'A', 'A', 0.0],
['A', 'A', 'B', 0.5],
['A', 'A', 'C', 0.5],
['A', 'B', 'A', 0.0],
['A', 'B', 'B', 0.0],
['A', 'B', 'C', 1.0],
['A', 'C', 'A', 0.0],
['A', 'C', 'B', 1.0],
['A', 'C', 'C', 0.0],
['B', 'A', 'A', 0.0],
['B', 'A', 'B', 0.0],
['B', 'A', 'C', 1.0],
['B', 'B', 'A', 0.5],
['B', 'B', 'B', 0.0],
['B', 'B', 'C', 0.5],
['B', 'C', 'A', 1.0],
['B', 'C', 'B', 0.0],
['B', 'C', 'C', 0.0],
['C', 'A', 'A', 0.0],
['C', 'A', 'B', 1.0],
['C', 'A', 'C', 0.0],
['C', 'B', 'A', 1.0],
['C', 'B', 'B', 0.0],
['C', 'B', 'C', 0.0],
['C', 'C', 'A', 0.5],
['C', 'C', 'B', 0.5],
['C', 'C', 'C', 0.0]], [guest, prize])
s1 = Node(guest, name="guest")
s2 = Node(prize, name="prize")
s3 = Node(monty, name="monty")
model = BayesianNetwork("Monty Hall Problem")
model.add_states(s1, s2, s3)
model.add_edge(s1, s3)
model.add_edge(s2, s3)
model.bake()
.. NOTE::
The objects 'state' and 'node' are really the same thing and can be used interchangeable. The only difference is the name, as hidden Markov models use 'state' in the literature frequently whereas Bayesian networks use 'node' frequently.
The conditional distribution must be explicitly spelled out in this example, followed by a list of the parents in the same order as the columns take in the table that is provided (e.g. the columns in the table correspond to guest, prize, monty, probability.)
However, one can also initialize a Bayesian network based completely on data. As mentioned before, the exact version of this algorithm takes exponential time with the number of variables and typically can't be done on more than ~25 variables. This is because there are a super-exponential number of directed acyclic graphs that one could define over a set of variables, but fortunately one can use dynamic programming in order to reduce this complexity down to "simply exponential." The implementation of the exact algorithm actually goes further than the original dynamic programming algorithm by implementing an A* search to somewhat reduce computational time but drastically reduce required memory, sometimes by an order of magnitude.
.. code-block:: python
from pomegranate import *
import numpy
X = numpy.load('data.npy')
model = BayesianNetwork.from_samples(X, algorithm='exact')
The exact algorithm is not the default, though. The default is a novel greedy algorithm that greedily chooses a topological ordering of the variables, but optimally identifies the best parents for each variable given this ordering. It is significantly faster and more memory efficient than the exact algorithm and produces far better estimates than using a Chow-Liu tree. This is set to the default to avoid locking up the computers of users that unintentionally tell their computers to do a near-impossible task.
Probability
-----------
You can calculate the probability of a sample under a Bayesian network as the product of the probability of each variable given its parents, if it has any. This can be expressed as :math:`P = \prod\limits_{i=1}^{d} P(D_{i}|Pa_{i})` for a sample with $d$ dimensions. For example, in the Monty Hal problem, the probability of a show is the probability of the guest choosing the respective door, times the probability of the prize being behind a given door, times the probability of Monty opening a given door given the previous two values. For example, using the manually initialized network above:
.. code-block:: python
>>> print(model.probability([['A', 'A', 'A'],
['A', 'A', 'B'],
['C', 'C', 'B']]))
[ 0. 0.05555556 0.05555556]
Prediction
----------
Bayesian networks are frequently used to infer/impute the value of missing variables given the observed values. In other models, typically there is either a single or fixed set of missing variables, such as latent factors, that need to be imputed, and so returning a fixed vector or matrix as the predictions makes sense. However, in the case of Bayesian networks, we can make no such assumptions, and so when data is passed in for prediction it should be in the format as a matrix with ``None`` in the missing variables that need to be inferred. The return is thus a filled in matrix where the Nones have been replaced with the imputed values. For example:
.. code-block:: python
>>> print(model.predict([['A', 'B', None],
['A', 'C', None],
['C', 'B', None]]))
[['A' 'B' 'C']
['A' 'C' 'B']
['C' 'B' 'A']]
In this example, the final column is the one that is always missing, but a more complex example is as follows:
.. code-block:: python
>>> print(model.predict([['A', 'B', None],
['A', None, 'C'],
[None, 'B', 'A']]))
[['A' 'B' 'C']
['A' 'B' 'C']
['C' 'B' 'A']]
Fitting
-------
Fitting a Bayesian network to data is a fairly simple process. Essentially, for each variable, you need consider only that column of data and the columns corresponding to that variables parents. If it is a univariate distribution, then the maximum likelihood estimate is just the count of each symbol divided by the number of samples in the data. If it is a multivariate distribution, it ends up being the probability of each symbol in the variable of interest given the combination of symbols in the parents. For example, consider a binary dataset with two variables, X and Y, where X is a parent of Y. First, we would go through the dataset and calculate P(X=0) and P(X=1). Then, we would calculate P(Y=0|X=0), P(Y=1|X=0), P(Y=0|X=1), and P(Y=1|X=1). Those values encode all of the parameters of the Bayesian network.
API Reference
-------------
.. automodule:: pomegranate.BayesianNetwork
:members:
:inherited-members:
pomegranate-0.13.5/docs/CODE_OF_CONDUCT.rst 0000664 0000000 0000000 00000007615 13740675601 0020063 0 ustar 00root root 0000000 0000000 ======
Code of Conduct
======
Our Pledge
----------
In the interest of fostering an open and welcoming environment, we as contributors and maintainers pledge to making participation in our project and our community a harassment-free experience for everyone, regardless of age, body size, disability, ethnicity, gender identity and expression, level of experience, nationality, personal appearance, race, religion, or sexual identity and orientation.
Our Standards
-------------
Examples of behavior that contributes to creating a positive environment include:
* Using welcoming and inclusive language
* Being respectful of differing viewpoints and experiences
* Gracefully accepting constructive criticism
* Focusing on what is best for the community
* Showing empathy towards other community members
Examples of unacceptable behavior by participants include:
* The use of sexualized language or imagery and unwelcome sexual attention or advances
* Trolling, insulting/derogatory comments, and personal or political attacks
* Public or private harassment
* Publishing others' private information, such as a physical or electronic address, without explicit permission
* Other conduct which could reasonably be considered inappropriate in a professional setting
Our Responsibilities
--------------------
Project maintainers are responsible for clarifying the standards of acceptable behavior and are expected to take appropriate and fair corrective action in response to any instances of unacceptable behavior.
Project maintainers have the right and responsibility to remove, edit, or reject comments, commits, code, wiki edits, issues, and other contributions that are not aligned to this Code of Conduct, or to ban temporarily or permanently any contributor for other behaviors that they deem inappropriate, threatening, offensive, or harmful.
Scope
-----
This Code of Conduct applies both within project spaces and in public spaces when an individual is representing the project or its community. Examples of representing a project or community include using an official project e-mail address, posting via an official social media account, or acting as an appointed representative at an online or offline event. Representation of a project may be further defined and clarified by project maintainers.
Enforcement
-----------
Instances of abusive, harassing, or otherwise unacceptable behavior may be reported by contacting the project team at jmschreiber91@gmail.com. Because the project team currently consists of only one member, that member shall investigate within one week whether a violation of the code of conduct occured and what the appropriate response is. That member shall then contact the original reporter and any other affected parties to explain the response and note feedback for the record. The project team is obligated to maintain confidentiality with regard to the reporter of an incident. Should you wish to file a report anonymously you should fill out a report at https://goo.gl/forms/aQtlDdrhZf4Y8flk2. If your report involves any members of the project team, if you feel uncomfortable making a report to the project team for any reason, or you feel that the issue has not been adequately handled, you are encouraged to send `your report `_ to conduct@numfocus.org where it will be independently reviewed by the `NumFOCUS team `_.
Project maintainers who do not follow or enforce the Code of Conduct in good faith may face temporary or permanent repercussions as determined by other members of the project's leadership.
Attribution
-----------
This Code of Conduct is adapted from the `Contributor Covenant homepage `_, `version 1\.4 `_.
For answers to common questions about this code of conduct, see https://www.contributor-covenant.org/faq.
pomegranate-0.13.5/docs/Distributions.rst 0000664 0000000 0000000 00000013401 13740675601 0020436 0 ustar 00root root 0000000 0000000 .. _distributions:
Probability Distributions
=========================
`IPython Notebook Tutorial `_
While probability distributions are frequently used as components of more complex models such as mixtures and hidden Markov models, they can also be used by themselves. Many data science tasks require fitting a distribution to data or generating samples under a distribution. pomegranate has a large library of both univariate and multivariate distributions which can be used with an intuitive interface.
**Univariate Distributions**
.. currentmodule:: pomegranate.distributions
.. autosummary::
UniformDistribution
BernoulliDistribution
NormalDistribution
LogNormalDistribution
ExponentialDistribution
PoissonDistribution
BetaDistribution
GammaDistribution
DiscreteDistribution
**Kernel Densities**
.. autosummary::
GaussianKernelDensity
UniformKernelDensity
TriangleKernelDensity
**Multivariate Distributions**
.. autosummary::
IndependentComponentsDistribution
MultivariateGaussianDistribution
DirichletDistribution
ConditionalProbabilityTable
JointProbabilityTable
While there are a large variety of univariate distributions, multivariate distributions can be made from univariate distributions by using ```IndependentComponentsDistribution``` with the assumption that each column of data is independent from the other columns (instead of being related by a covariance matrix, like in multivariate gaussians). Here is an example:
.. code-block:: python
d1 = NormalDistribution(5, 2)
d2 = LogNormalDistribution(1, 0.3)
d3 = ExponentialDistribution(4)
d = IndependentComponentsDistribution([d1, d2, d3])
Use MultivariateGaussianDistribution when you want the full correlation matrix within the feature vector. When you want a strict diagonal correlation (i.e no correlation or "independent"), this is achieved using IndependentComponentsDistribution with NormalDistribution for each feature. There is no implementation of spherical or other variations of correlation.
Initialization
--------------
Initializing a distribution is simple and done just by passing in the distribution parameters. For example, the parameters of a normal distribution are the mean (mu) and the standard deviation (sigma). We can initialize it as follows:
.. code-block:: python
from pomegranate import *
a = NormalDistribution(5, 2)
However, frequently we don't know the parameters of the distribution beforehand or would like to directly fit this distribution to some data. We can do this through the `from_samples` class method.
.. code-block:: python
b = NormalDistribution.from_samples([3, 4, 5, 6, 7])
If we want to fit the model to weighted samples, we can just pass in an array of the relative weights of each sample as well.
.. code-block:: python
b = NormalDistribution.from_samples([3, 4, 5, 6, 7], weights=[0.5, 1, 1.5, 1, 0.5])
Probability
-----------
Distributions are typically used to calculate the probability of some sample. This can be done using either the `probability` or `log_probability` methods.
.. code-block:: python
>>> a = NormalDistribution(5, 2)
>>> a.log_probability(8)
-2.737085713764219
>>> a.probability(8)
0.064758797832971712
>>> b = NormalDistribution.from_samples([3, 4, 5, 6, 7], weights=[0.5, 1, 1.5, 1, 0.5])
>>> b.log_probability(8)
-4.437779569430167
These methods work for univariate distributions, kernel densities, and multivariate distributions all the same. For a multivariate distribution you'll have to pass in an array for the full sample.
.. code-block:: python
>>> d1 = NormalDistribution(5, 2)
>>> d2 = LogNormalDistribution(1, 0.3)
>>> d3 = ExponentialDistribution(4)
>>> d = IndependentComponentsDistribution([d1, d2, d3])
>>>
>>> X = [6.2, 0.4, 0.9]
>>> d.log_probability(X)
-23.205411733352875
Fitting
-------
We may wish to fit the distribution to new data, either overriding the previous parameters completely or moving the parameters to match the dataset more closely through inertia. Distributions are updated using maximum likelihood estimates (MLE). Kernel densities will either discard previous points or downweight them if inertia is used.
.. code-block:: python
d = NormalDistribution(5, 2)
d.fit([1, 5, 7, 3, 2, 4, 3, 5, 7, 8, 2, 4, 6, 7, 2, 4, 5, 1, 3, 2, 1])
d
{
"frozen" :false,
"class" :"Distribution",
"parameters" :[
3.9047619047619047,
2.13596776114341
],
"name" :"NormalDistribution"
}
Training can be done on weighted samples by passing an array of weights in along with the data for any of the training functions, like the following:
.. code-block:: python
d = NormalDistribution(5, 2)
d.fit([1, 5, 7, 3, 2, 4], weights=[0.5, 0.75, 1, 1.25, 1.8, 0.33])
d
{
"frozen" :false,
"class" :"Distribution",
"parameters" :[
3.538188277087034,
1.954149818564894
],
"name" :"NormalDistribution"
}
Training can also be done with inertia, where the new value will be some percentage the old value and some percentage the new value, used like `d.from_samples([5,7,8], inertia=0.5)` to indicate a 50-50 split between old and new values.
API Reference
-------------
.. automodule:: pomegranate.distributions
:members: BernoulliDistribution,BetaDistribution,ConditionalProbabilityTable,DirichletDistribution,DiscreteDistribution,ExponentialDistribution,GammaDistribution,IndependentComponentsDistribution,JointProbabilityTable,KernelDensities,LogNormalDistribution,MultivariateGaussianDistribution,NormalDistribution,PoissonDistribution,UniformDistribution
pomegranate-0.13.5/docs/FactorGraph.rst 0000664 0000000 0000000 00000000177 13740675601 0020002 0 ustar 00root root 0000000 0000000 .. _factorgraph:
Factor Graphs
=============
API Reference
-------------
.. automodule:: pomegranate.FactorGraph
:members:
pomegranate-0.13.5/docs/GeneralMixtureModel.rst 0000664 0000000 0000000 00000014036 13740675601 0021515 0 ustar 00root root 0000000 0000000 .. _generalmixturemodel:
General Mixture Models
======================
`IPython Notebook Tutorial `_
General Mixture models (GMMs) are an unsupervised probabilistic model composed of multiple distributions (commonly referred to as components) and corresponding weights. This allows you to model more complex distributions corresponding to a singular underlying phenomena. For a full tutorial on what a mixture model is and how to use them, see the above tutorial.
Initialization
--------------
General Mixture Models can be initialized in two ways depending on if you know the initial parameters of the model or not: (1) passing in a list of pre-initialized distributions, or (2) running the ``from_samples`` class method on data. The initial parameters can be either a pre-specified model that is ready to be used for prediction, or the initialization for expectation-maximization. Otherwise, if the second initialization option is chosen, then k-means is used to initialize the distributions. The distributions passed for each component don't have to be the same type, and if an ``IndependentComponentDistribution`` object is passed in, then the dimensions don't need to be modeled by the same distribution.
Here is an example of a traditional multivariate Gaussian mixture where we pass in pre-initialized distributions. We can also pass in the weight of each component, which serves as the prior probability of a sample belonging to that component when doing predictions.
.. code-block:: python
>>> from pomegranate import *
>>> d1 = MultivariateGaussianDistribution([1, 6, 3], [[1, 0, 0], [0, 1, 0], [0, 0, 1]])
>>> d2 = MultivariateGaussianDistribution([2, 8, 4], [[1, 0, 0], [0, 1, 0], [0, 0, 2]])
>>> d3 = MultivariateGaussianDistribution([0, 4, 8], [[2, 0, 0], [0, 3, 0], [0, 0, 1]])
>>> model = GeneralMixtureModel([d1, d2, d3], weights=[0.25, 0.60, 0.15])
Alternatively, if we want to model each dimension differently, then we can replace the multivariate Gaussian distributions with ``IndependentComponentsDistribution`` objects.
.. code-block:: python
>>> from pomegranate import *
>>> d1 = IndependentComponentsDistribution([NormalDistribution(5, 2), ExponentialDistribution(1), LogNormalDistribution(0.4, 0.1)])
>>> d2 = IndependentComponentsDistribution([NormalDistribution(3, 1), ExponentialDistribution(2), LogNormalDistribution(0.8, 0.2)])
>>> model = GeneralMixtureModel([d1, d2], weights=[0.66, 0.34])
If we do not know the parameters of our distributions beforehand and want to learn them entirely from data, then we can use the ``from_samples`` class method. This method will run k-means to initialize the components, using the returned clusters to initialize all parameters of the distributions, i.e. both mean and covariances for multivariate Gaussian distributions. Afterwards, expectation-maximization is used to refine the parameters of the model, iterating until convergence.
.. code-block:: python
>>> from pomegranate import *
>>> model = GeneralMixtureModel.from_samples(MultivariateGaussianDistribution, n_components=3, X=X)
If we want to model each dimension using a different distribution, then we can pass in a list of callables and they will be initialized using k-means as well.
.. code-block:: python
>>> from pomegranate import *
>>> model = GeneralMixtureModel.from_samples([NormalDistribution, ExponentialDistribution, LogNormalDistribution], n_components=5, X=X)
Probability
---------------
The probability of a point is the sum of its probability under each of the components, multiplied by the weight of each component c, :math:`P = \sum\limits_{i \in M} P(D|M_{i})P(M_{i})`. The ``probability`` method returns the probability of each sample under the entire mixture, and the ``log_probability`` method returns the log of that value.
Prediction
----------
The common prediction tasks involve predicting which component a new point falls under. This is done using Bayes rule :math:`P(M|D) = \frac{P(D|M)P(M)}{P(D)}` to determine the posterior probability :math:`P(M|D)` as opposed to simply the likelihood :math:`P(D|M)`. Bayes rule indicates that it isn't simply the likelihood function which makes this prediction but the likelihood function multiplied by the probability that that distribution generated the sample. For example, if you have a distribution which has 100x as many samples fall under it, you would naively think that there is a ~99% chance that any random point would be drawn from it. Your belief would then be updated based on how well the point fit each distribution, but the proportion of points generated by each sample is important as well.
We can get the component label assignments using ``model.predict(data)``, which will return an array of indexes corresponding to the maximally likely component. If what we want is the full matrix of :math:`P(M|D)`, then we can use ``model.predict_proba(data)``, which will return a matrix with each row being a sample, each column being a component, and each cell being the probability that that model generated that data. If we want log probabilities instead we can use ``model.predict_log_proba(data)`` instead.
Fitting
-------
Training GMMs faces the classic chicken-and-egg problem that most unsupervised learning algorithms face. If we knew which component a sample belonged to, we could use MLE estimates to update the component. And if we knew the parameters of the components we could predict which sample belonged to which component. This problem is solved using expectation-maximization, which iterates between the two until convergence. In essence, an initialization point is chosen which usually is not a very good start, but through successive iteration steps, the parameters converge to a good ending.
These models are fit using ``model.fit(data)``. A maximum number of iterations can be specified as well as a stopping threshold for the improvement ratio. See the API reference for full documentation.
API Reference
-------------
.. automodule:: pomegranate.gmm
:members:
:inherited-members:
pomegranate-0.13.5/docs/HiddenMarkovModel.rst 0000664 0000000 0000000 00000025462 13740675601 0021142 0 ustar 00root root 0000000 0000000 .. _hiddenmarkovmodel:
Hidden Markov Models
====================
- `IPython Notebook Tutorial `_
- `IPython Notebook Sequence Alignment Tutorial `_
`Hidden Markov models `_ (HMMs) are a structured probabilistic model that forms a probability distribution of sequences, as opposed to individual symbols. It is similar to a Bayesian network in that it has a directed graphical structure where nodes represent probability distributions, but unlike Bayesian networks in that the edges represent transitions and encode transition probabilities, whereas in Bayesian networks edges encode dependence statements. A HMM can be thought of as a general mixture model plus a transition matrix, where each component in the general Mixture model corresponds to a node in the hidden Markov model, and the transition matrix informs the probability that adjacent symbols in the sequence transition from being generated from one component to another. A strength of HMMs is that they can model variable length sequences whereas other models typically require a fixed feature set. They are extensively used in the fields of natural language processing to model speech, bioinformatics to model biosequences, and robotics to model movement.
The HMM implementation in pomegranate is based off of the implementation in its predecessor, Yet Another Hidden Markov Model (YAHMM). To convert a script that used YAHMM to a script using pomegranate, you only need to change calls to the ``Model`` class to call ``HiddenMarkovModel``. For example, a script that previously looked like the following:
.. code-block:: python
from yahmm import *
model = Model()
would now be written as
.. code-block:: python
from pomegranate import *
model = HiddenMarkovModel()
and the remaining method calls should be identical.
Initialization
--------------
Hidden Markov models can be initialized in one of two ways depending on if you know the initial parameters of the model, either (1) by defining both the distributions and the graphical structure manually, or (2) running the ``from_samples`` method to learn both the structure and distributions directly from data. The first initialization method can be used either to specify a pre-defined model that is ready to make predictions, or as the initialization to a training algorithm such as Baum-Welch. It is flexible enough to allow sparse transition matrices and any type of distribution on each node, i.e. normal distributions on several nodes, but a mixture of normals on some nodes modeling more complex phenomena. The second initialization method is less flexible, in that currently each node must have the same distribution type, and that it will only learn dense graphs. Similar to mixture models, this initialization method starts with k-means to initialize the distributions and a uniform probability transition matrix before running Baum-Welch.
If you are initializing the parameters manually, you can do so either by passing in a list of distributions and a transition matrix, or by building the model line-by-line. Let's first take a look at building the model from a list of distributions and a transition matrix.
.. code-block:: python
from pomegranate import *
dists = [NormalDistribution(5, 1), NormalDistribution(1, 7), NormalDistribution(8,2)]
trans_mat = numpy.array([[0.7, 0.3, 0.0],
[0.0, 0.8, 0.2],
[0.0, 0.0, 0.9]])
starts = numpy.array([1.0, 0.0, 0.0])
ends = numpy.array([0.0, 0.0, 0.1])
model = HiddenMarkovModel.from_matrix(trans_mat, dists, starts, ends)
Next, let's take a look at building the same model line by line.
.. code-block:: python
from pomegranate import *
s1 = State(NormalDistribution(5, 1))
s2 = State(NormalDistribution(1, 7))
s3 = State(NormalDistribution(8, 2))
model = HiddenMarkovModel()
model.add_states(s1, s2, s3)
model.add_transition(model.start, s1, 1.0)
model.add_transition(s1, s1, 0.7)
model.add_transition(s1, s2, 0.3)
model.add_transition(s2, s2, 0.8)
model.add_transition(s2, s3, 0.2)
model.add_transition(s3, s3, 0.9)
model.add_transition(s3, model.end, 0.1)
model.bake()
Initially it may seem that the first method is far easier due to it being fewer lines of code. However, when building large sparse models defining a full transition matrix can be cumbersome, especially when it is mostly 0s.
Models built in this manner must be explicitly "baked" at the end. This finalizes the model topology and creates the internal sparse matrix which makes up the model. This step also automatically normalizes all transitions to make sure they sum to 1.0, stores information about tied distributions, edges, pseudocounts, and merges unnecessary silent states in the model for computational efficiency. This can cause the `bake` step to take a little bit of time. If you want to reduce this overhead and are sure you specified the model correctly you can pass in `merge="None"` to the bake step to avoid model checking.
The second way to initialize models is to use the ``from_samples`` class method. The call is identical to initializing a mixture model.
.. code-block:: python
>>> from pomegranate import *
>>> model = HiddenMarkovModel.from_samples(NormalDistribution, n_components=5, X=X)
Much like a mixture model, all arguments present in the ``fit`` step can also be passed in to this method. Also like a mixture model, it is initialized by running k-means on the concatenation of all data, ignoring that the symbols are part of a structured sequence. The clusters returned are used to initialize all parameters of the distributions, i.e. both mean and covariances for multivariate Gaussian distributions. The transition matrix is initialized as uniform random probabilities. After the components (distributions on the nodes) are initialized, the given training algorithm is used to refine the parameters of the distributions and learn the appropriate transition probabilities.
Log Probability
---------------
There are two common forms of the log probability which are used. The first is the log probability of the most likely path the sequence can take through the model, called the Viterbi probability. This can be calculated using ``model.viterbi(sequence)``. However, this is :math:`P(D|S_{ML}, S_{ML}, S_{ML})` not :math:`P(D|M)`. In order to get :math:`P(D|M)` we have to sum over all possible paths instead of just the single most likely path. This can be calculated using ``model.log_probability(sequence)`` and uses the forward algorithm internally. On that note, the full forward matrix can be returned using ``model.forward(sequence)`` and the full backward matrix can be returned using ``model.backward(sequence)``, while the full forward-backward emission and transition matrices can be returned using ``model.forward_backward(sequence)``.
Prediction
----------
A common prediction technique is calculating the Viterbi path, which is the most likely sequence of states that generated the sequence given the full model. This is solved using a simple dynamic programming algorithm similar to sequence alignment in bioinformatics. This can be called using ``model.viterbi(sequence)``. A sklearn wrapper can be called using ``model.predict(sequence, algorithm='viterbi')``.
Another prediction technique is called maximum a posteriori or forward-backward, which uses the forward and backward algorithms to calculate the most likely state per observation in the sequence given the entire remaining alignment. Much like the forward algorithm can calculate the sum-of-all-paths probability instead of the most likely single path, the forward-backward algorithm calculates the best sum-of-all-paths state assignment instead of calculating the single best path. This can be called using ``model.predict(sequence, algorithm='map')`` and the raw normalized probability matrices can be called using ``model.predict_proba(sequence)``.
Fitting
-------
A simple fitting algorithm for hidden Markov models is called Viterbi training. In this method, each observation is tagged with the most likely state to generate it using the Viterbi algorithm. The distributions (emissions) of each states are then updated using MLE estimates on the observations which were generated from them, and the transition matrix is updated by looking at pairs of adjacent state taggings. This can be done using ``model.fit(sequence, algorithm='viterbi')``.
However, this is not the best way to do training and much like the other sections there is a way of doing training using sum-of-all-paths probabilities instead of maximally likely path. This is called Baum-Welch or forward-backward training. Instead of using hard assignments based on the Viterbi path, observations are given weights equal to the probability of them having been generated by that state. Weighted MLE can then be done to update the distributions, and the soft transition matrix can give a more precise probability estimate. This is the default training algorithm, and can be called using either ``model.fit(sequences)`` or explicitly using ``model.fit(sequences, algorithm='baum-welch')``.
pomegranate also supports labeled training of hidden Markov models. This setting is where one has state labels for each observation and wishes to derive the transition matrix and observations given those labels. The emissions simply become MLE estimates of the data partitioned by the labels and the transition matrix is calculated directly from the adjacency of labels. This option can be specified using ``model.fit(sequences, labels=labels, state_names=state_names)`` where ``labels`` has the same shape as ``sequences`` and ``state_names`` has the set of all possible labels.
.. note::
The sequence of labels can include hidden states! However, a consequence of this is that each sequence of labels must begin with the start state because that is where each sequence begins with being aligned to the model. For instance, for the sequence of observations ``[1, 5, 6, 2]`` the corresponding labels would be ``['None-start', 'a', 'b', 'b', 'a']`` because the default name of a model is ``None`` and the name of the start state is ``{name}-start``. Likewise, you will need to add the end state label at the end of each sequence if you want an explicit end state, making the labels ``['None-start', 'a', 'b', 'b', 'a', 'None-end']``.
There are a number of optional parameters that provide more control over the training process, including the use of distribution or edge inertia, freezing certain states, tying distributions or edges, and using pseudocounts. See the tutorial linked to at the top of this page for full details on each of these options.
API Reference
-------------
.. automodule:: pomegranate.hmm
:members:
:inherited-members:
pomegranate-0.13.5/docs/Makefile 0000664 0000000 0000000 00000016774 13740675601 0016522 0 ustar 00root root 0000000 0000000 # Makefile for Sphinx documentation
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pomegranate-0.13.5/docs/MarkovChain.rst 0000664 0000000 0000000 00000006050 13740675601 0020000 0 ustar 00root root 0000000 0000000 .. _markovchain:
Markov Chains
=============
`IPython Notebook Tutorial `_
Markov chains are form of structured model over sequences. They represent the probability of each character in the sequence as a conditional probability of the last k symbols. For example, a 3rd order Markov chain would have each symbol depend on the last three symbols. A 0th order Markov chain is a naive predictor where each symbol is independent of all other symbols. Currently pomegranate only supports discrete emission Markov chains where each symbol is a discrete symbol versus a continuous number (like 'A' 'B' 'C' instead of 17.32 or 19.65).
Initialization
--------------
Markov chains can almost be represented by a single conditional probability table (CPT), except that the probability of the first k elements (for a k-th order Markov chain) cannot be appropriately represented except by using special characters. Due to this pomegranate takes in a series of k+1 distributions representing the first k elements. For example for a second order Markov chain:
.. code-block:: python
from pomegranate import *
d1 = DiscreteDistribution({'A': 0.25, 'B': 0.75})
d2 = ConditionalProbabilityTable([['A', 'A', 0.1],
['A', 'B', 0.9],
['B', 'A', 0.6],
['B', 'B', 0.4]], [d1])
d3 = ConditionalProbabilityTable([['A', 'A', 'A', 0.4],
['A', 'A', 'B', 0.6],
['A', 'B', 'A', 0.8],
['A', 'B', 'B', 0.2],
['B', 'A', 'A', 0.9],
['B', 'A', 'B', 0.1],
['B', 'B', 'A', 0.2],
['B', 'B', 'B', 0.8]], [d1, d2])
model = MarkovChain([d1, d2, d3])
Probability
-----------
The probability of a sequence under the Markov chain is just the probability of the first character under the first distribution times the probability of the second character under the second distribution and so forth until you go past the (k+1)th character, which remains evaluated under the (k+1)th distribution. We can calculate the probability or log probability in the same manner as any of the other models. Given the model shown before:
.. code-block:: python
>>> model.log_probability(['A', 'B', 'B', 'B'])
-3.324236340526027
>>> model.log_probability(['A', 'A', 'A', 'A'])
-5.521460917862246
Fitting
-------
Markov chains are not very complicated to train. For each sequence the appropriate symbols are sent to the appropriate distributions and maximum likelihood estimates are used to update the parameters of the distributions. There are no latent factors to train and so no expectation maximization or iterative algorithms are needed to train anything.
API Reference
-------------
.. automodule:: pomegranate.MarkovChain
:members:
:inherited-members:
pomegranate-0.13.5/docs/MarkovNetwork.rst 0000664 0000000 0000000 00000012736 13740675601 0020417 0 ustar 00root root 0000000 0000000 .. _markovnetwork:
Markov Networks
===============
- `IPython Notebook Tutorial `_
`Markov networks `_ (sometimes called Markov random fields) are probabilistic models that are typically represented using an undirected graph. Each of the nodes in the graph represents a variable in the data and each of the edges represent an associate. Unlike Bayesian networks which have directed edges and clear directions of causality, Markov networks have undirected edges and only encode associations.
Currently, pomegranate only supports discrete Markov networks, meaning that the values must be categories, i.e. 'apples' and 'oranges', or 1 and 2, where 1 and 2 refer to categories, not numbers, and so 2 is not explicitly 'bigger' than 1.
Initialization
--------------
Markov networks can be initialized in two ways, depending on whether the underlying graphical structure is known or not: (1) a list of the joint probabilities tables can be passed into the initialization, with one table per clique in the graph, or (2) both the graphical structure and distributions can be learned directly from data. This mirrors the other models that are implemented in pomegranate. However, because finding the optimal Markov network requires enumerating a number of potential graphs that is exponential with the number of dimensions in the data, it can be fairly time intensive to find the exact network.
Let's see an example of creating a Markov network with three cliques in it.
.. code-block:: python
from pomegranate import *
d1 = JointProbabilityTable([
[0, 0, 0.1],
[0, 1, 0.2],
[1, 0, 0.4],
[1, 1, 0.3]], [0, 1])
d2 = JointProbabilityTable([
[0, 0, 0, 0.05],
[0, 0, 1, 0.15],
[0, 1, 0, 0.07],
[0, 1, 1, 0.03],
[1, 0, 0, 0.12],
[1, 0, 1, 0.18],
[1, 1, 0, 0.10],
[1, 1, 1, 0.30]], [1, 2, 3])
d3 = JointProbabilityTable([
[0, 0, 0, 0.08],
[0, 0, 1, 0.12],
[0, 1, 0, 0.11],
[0, 1, 1, 0.19],
[1, 0, 0, 0.04],
[1, 0, 1, 0.06],
[1, 1, 0, 0.23],
[1, 1, 1, 0.17]], [2, 3, 4])
model = MarkovNetwork([d1, d2, d3])
model.bake()
That was fairly simple. Each `JointProbabilityTable` object just had to include the table of all values that the variables can take as well as a list of variable indexes that are included in the table, in the order from left to right that they appear. For example, in d1, the first column of the table corresponds to the first column of data in a data matrix and the second column in the table corresponds to the second column in a data matrix.
One can also initialize a Markov network based completely on data. Currently, the only algorithm that pomegranate supports for this is the Chow-Liu tree-building algorithm. This algorithm first calculates the mutual information between all pairs of variables and then determines the maximum spanning tree through it. This process generally captures the strongest dependencies in the data set. However, because it requires all variables to have at least one connection, it can lead to instances where variables are incorrectly associated with each other. Overall, it generally performs well and it fairly fast to calculate.
.. code-block:: python
from pomegranate import *
import numpy
X = numpy.random.randint(2, size=(100, 6))
model = MarkovNetwork.from_samples(X)
Probability
-----------
The probability of an example under a Markov network is more difficult to calculate than under a Bayesian network. With a Bayesian network, one can simply multiply the probabilities of each variable given its parents to get a probability of the entire example. However, repeating this process for a Markov network (by plugging in the values of each clique and multiplying across all cliques) results in a value called the "unnormalized" probability. This value is called "unnormalized" because the sum of this value across all combinations of values that the variables in an example can take does not sum to 1.
The normalization of an "unnormalized" probability requires the calculation of a partition function. This function (frequently abbreviated `Z`) is just the sum of the probability of all combinations of values that the variables can take. After calculation, one can just divide the unnormalized probability by this value to get the normalized probability. The only problem is that the calculation of the partition function requires the summation over a number of examples that grows exponentially with the number of dimensions. You can read more about this in the tutorial.
If you have a small number of variables (<30) it shouldn't be a problem to calculate the partition function and then normalized probabilities.
.. code-block:: python
>>> print(model.probability([1, 0, 1, 0, 1]))
-4.429966143312331
Prediction
----------
Markov networks can be used to predict the value of missing variables given the observed values in a process called "inference." In other predictive models there are typically a single or fixed set of missing values that need to be predicted, commonly referred to as the labels. However, in the case of Markov (or Bayesian) networks, the missing values can be any variables and the inference process will use all of the available data to impute those missing values. For example:
.. code-block:: python
>>> print(model.predict([[None, 0, None, 1, None]]))
[[1, 0, 0, 1, 1]]
API Reference
-------------
.. automodule:: pomegranate.MarkovNetwork
:members:
:inherited-members:
pomegranate-0.13.5/docs/NaiveBayes.rst 0000664 0000000 0000000 00000021714 13740675601 0017630 0 ustar 00root root 0000000 0000000 .. _naivebayes:
Bayes Classifiers and Naive Bayes
=================================
`IPython Notebook Tutorial `_
Bayes classifiers are simple probabilistic classification models based off of Bayes theorem. See the above tutorial for a full primer on how they work, and what the distinction between a naive Bayes classifier and a Bayes classifier is. Essentially, each class is modeled by a probability distribution and classifications are made according to what distribution fits the data the best. They are a supervised version of general mixture models, in that the ``predict``, ``predict_proba``, and ``predict_log_proba`` methods return the same values for the same underlying distributions, but that instead of using expectation-maximization to fit to new data they can use the provided labels directly.
Initialization
--------------
Bayes classifiers and naive Bayes can both be initialized in one of two ways depending on if you know the parameters of the model beforehand or not, (1) passing in a list of pre-initialized distributions to the model, or (2) using the ``from_samples`` class method to initialize the model directly from data. For naive Bayes models on multivariate data, the pre-initialized distributions must be a list of ``IndependentComponentDistribution`` objects since each dimension is modeled independently from the others. For Bayes classifiers on multivariate data a list of any type of multivariate distribution can be provided. For univariate data the two models produce identical results, and can be passed in a list of univariate distributions. For example:
.. code-block:: python
from pomegranate import *
d1 = IndependentComponentsDistribution([NormalDistribution(5, 2), NormalDistribution(6, 1), NormalDistribution(9, 1)])
d2 = IndependentComponentsDistribution([NormalDistribution(2, 1), NormalDistribution(8, 1), NormalDistribution(5, 1)])
d3 = IndependentComponentsDistribution([NormalDistribution(3, 1), NormalDistribution(5, 3), NormalDistribution(4, 1)])
model = NaiveBayes([d1, d2, d3])
would create a three class naive Bayes classifier that modeled data with three dimensions. Alternatively, we can initialize a Bayes classifier in the following manner
.. code-block:: python
from pomegranate import *
d1 = MultivariateGaussianDistribution([5, 6, 9], [[2, 0, 0], [0, 1, 0], [0, 0, 1]])
d2 = MultivariateGaussianDistribution([2, 8, 5], [[1, 0, 0], [0, 1, 0], [0, 0, 1]])
d3 = MultivariateGaussianDistribution([3, 5, 4], [[1, 0, 0], [0, 3, 0], [0, 0, 1]])
model = BayesClassifier([d1, d2, d3])
The two examples above functionally create the same model, as the Bayes classifier uses multivariate Gaussian distributions with the same means and a diagonal covariance matrix containing only the variances. However, if we were to fit these models to data later on, the Bayes classifier would learn a full covariance matrix while the naive Bayes would only learn the diagonal.
If we instead wish to initialize our model directly onto data, we use the ``from_samples`` class method.
.. code-block:: python
from pomegranate import *
import numpy
X = numpy.load('data.npy')
y = numpy.load('labels.npy')
model = NaiveBayes.from_samples(NormalDistribution, X, y)
This would create a naive Bayes model directly from the data with normal distributions modeling each of the dimensions, and a number of components equal to the number of classes in ``y``. Alternatively if we wanted to create a model with different distributions for each dimension we can do the following:
.. code-block:: python
>>> model = NaiveBayes.from_samples([NormalDistribution, ExponentialDistribution], X, y)
This assumes that your data is two dimensional and that you want to model the first distribution as a normal distribution and the second dimension as an exponential distribution.
We can do pretty much the same thing with Bayes classifiers, except passing in a more complex model.
.. code-block:: python
>>> model = BayesClassifier.from_samples(MultivariateGaussianDistribution, X, y)
One can use much more complex models than just a multivariate Gaussian with a full covariance matrix when using a Bayes classifier. Specifically, you can also have your distributions be general mixture models, hidden Markov models, and Bayesian networks. For example:
.. code-block:: python
>>> model = BayesClassifier.from_samples(BayesianNetwork, X, y)
That would require that the data is only discrete valued currently, and the structure learning task may be too long if not set appropriately. However, it is possible. Currently, one cannot simply put in GeneralMixtureModel or HiddenMarkovModel despite them having a ``from_samples`` method because there is a great deal of flexibility in terms of the structure or emission distributions. The easiest way to set up one of these more complex models is to build each of the components separately and then feed them into the Bayes classifier method using the first initialization method.
.. code-block:: python
>>> d1 = GeneralMixtureModel.from_samples(MultivariateGaussianDistribution, n_components=5, X=X[y==0])
>>> d2 = GeneralMixtureModel.from_samples(MultivariateGaussianDistribution, n_components=5, X=X[y==1])
>>> model = BayesClassifier([d1, d2])
Prediction
----------
Bayes classifiers and naive Bayes supports the same three prediction methods that the other models support, ``predict``, ``predict_proba``, and ``predict_log_proba``. These methods return the most likely class given the data (argmax_m P(M|D)), the probability of each class given the data (P(M|D)), and the log probability of each class given the data (log P(M|D)). It is best to always pass in a 2D matrix even for univariate data, where it would have a shape of (n, 1).
The ``predict`` method takes in samples and returns the most likely class given the data.
.. code-block:: python
from pomegranate import *
model = NaiveBayes([NormalDistribution(5, 2), UniformDistribution(0, 10), ExponentialDistribution(1.0)])
model.predict( np.array([[0], [1], [2], [3], [4]]))
[2, 2, 2, 0, 0]
Calling ``predict_proba`` on five samples for a Naive Bayes with univariate components would look like the following.
.. code-block:: python
from pomegranate import *
model = NaiveBayes([NormalDistribution(5, 2), UniformDistribution(0, 10), ExponentialDistribution(1)])
model.predict_proba(np.array([[0], [1], [2], [3], [4]]))
[[ 0.00790443 0.09019051 0.90190506]
[ 0.05455011 0.20207126 0.74337863]
[ 0.21579499 0.33322883 0.45097618]
[ 0.44681566 0.36931382 0.18387052]
[ 0.59804205 0.33973357 0.06222437]]
Multivariate models work the same way.
.. code-block:: python
from pomegranate import *
d1 = MultivariateGaussianDistribution([5, 5], [[1, 0], [0, 1]])
d2 = IndependentComponentsDistribution([NormalDistribution(5, 2), NormalDistribution(5, 2)])
model = BayesClassifier([d1, d2])
clf.predict_proba(np.array([[0, 4],
[1, 3],
[2, 2],
[3, 1],
[4, 0]]))
array([[ 0.00023312, 0.99976688],
[ 0.00220745, 0.99779255],
[ 0.00466169, 0.99533831],
[ 0.00220745, 0.99779255],
[ 0.00023312, 0.99976688]])
``predict_log_proba`` works the same way, returning the log probabilities instead of the probabilities.
Fitting
-------
Both naive Bayes and Bayes classifiers also have a ``fit`` method that updates the parameters of the model based on new data. The major difference between these methods and the others presented is that these are supervised methods and so need to be passed labels in addition to data. This change propagates also to the ``summarize`` method, where labels are provided as well.
.. code-block:: python
from pomegranate import *
d1 = MultivariateGaussianDistribution([5, 5], [[1, 0], [0, 1]])
d2 = IndependentComponentsDistribution(NormalDistribution(5, 2), NormalDistribution(5, 2)])
model = BayesClassifier([d1, d2])
X = np.array([[6.0, 5.0],
[3.5, 4.0],
[7.5, 1.5],
[7.0, 7.0 ]])
y = np.array([0, 0, 1, 1])
model.fit(X, y)
As we can see, there are four samples, with the first two samples labeled as class 0 and the last two samples labeled as class 1. Keep in mind that the training samples must match the input requirements for the models used. So if using a univariate distribution, then each sample must contain one item. A bivariate distribution, two. For hidden markov models, the sample can be a list of observations of any length. An example using hidden markov models would be the following.
.. code-block:: python
d1 = HiddenMarkovModel...
d2 = HiddenMarkovModel...
d3 = HiddenMarkovModel...
model = BayesClassifier([d1, d2, d3])
X = np.array([list('HHHHHTHTHTTTTH'),
list('HHTHHTTHHHHHTH'),
list('TH'),
list('HHHHT')])
y = np.array([2, 2, 1, 0])
model.fit(X, y)
API Reference
-------------
.. automodule:: pomegranate.NaiveBayes
:members:
:inherited-members:
.. automodule:: pomegranate.BayesClassifier
:members:
:inherited-members:
pomegranate-0.13.5/docs/_templates/ 0000775 0000000 0000000 00000000000 13740675601 0017200 5 ustar 00root root 0000000 0000000 pomegranate-0.13.5/docs/_templates/class.rst 0000664 0000000 0000000 00000000244 13740675601 0021037 0 ustar 00root root 0000000 0000000 {{ fullname }}
{{ underline }}
.. currentmodule:: {{ module }}
.. autoclass:: {{ objname }}
{% block methods %}
.. automethod:: __init__
{% endblock %}
pomegranate-0.13.5/docs/api.rst 0000664 0000000 0000000 00000010474 13740675601 0016354 0 ustar 00root root 0000000 0000000 =======
The API
=======
pomegranate has a minimal core API that is made possible because all models are treated as a probability distribution regardless of complexity. Regardless of whether it's a simple probability distribution, or a hidden Markov model that uses a different probability distribution on each feature, these methods can be used. Each model documentation page has an API reference showing the full set of methods and parameters for each method, but generally all models have the following methods and parameters for the methods.
.. code-block:: python
>>> model.probability(X)
This method will take in either a single sample and return its probability, or a set of samples and return the probability of each one, given the model.
.. code-block:: python
>>> model.log_probability(X)
The same as above but returns the log of the probability. This is helpful for numeric stability.
.. code-block:: python
>>> model.fit(X, weights=None, inertia=0.0)
This will fit the model to the given data with optional weights. If called on a mixture model or a hidden Markov model this runs expectation-maximization to perform iterative updates, otherwise it uses maximum likelihood estimates. The shape of data should be (n, d) where n is the number of samples and d is the dimensionality, with weights being a vector of non-negative numbers of size (n,) when passed in. The inertia shows the proportion of the prior weight to use, defaulting to ignoring the prior values.
.. code-block:: python
>>> model.summarize(X, weights=None)
This is the first step of the two step out-of-core learning API. It will take in a data set and optional weights and extract the sufficient statistics that allow for an exact update, adding to the cached values. If this is the first time that summarize is called then it will store the extracted values, if it's not the first time then the extracted values are added to those that have already been cached.
.. code-block:: python
>>> model.from_summaries(inertia=0.0)
This is the second step in the out-of-core learning API. It will used the extracted and aggregated sufficient statistics to derive exact parameter updates for the model. Afterwards it will reset the stored values.
.. code-block:: python
>>> model.clear_summaries()
This method clears whatever summaries are left on the model without updating the parameters.
.. code-block:: python
>>> Model.from_samples(X, weights=None)
This method will initialize a model to a data set. In the case of a simple distribution it will simply extract the parameters from the case. In the more complicated case of a Bayesian network it will jointly find the best structure and the best parameters given that structure. In the case of a hidden Markov model it will first find clusters and then learn a dense transition matrix.
Compositional Methods
---------------------
These methods are available for the compositional models, i.e., mixture models, hidden Markov models, Bayesian networks, naive Bayes classifiers, and Bayes' classifiers. These methods perform inference on the data. In the case of Bayesian networks it will use the forward-backward algorithm to make predictions on all variables for which values are not provided. For all other models, this will return the model component that yields the highest posterior P(M|D) for some sample. This value is calculated using Bayes' rule, where the likelihood of each sample given each component multiplied by the prior of that component is normalized by the likelihood of that sample given all components multiplied by the prior of those components.
.. code-block:: python
>>> model.predict(X)
This will return the most likely value for the data. In the case of Bayesian networks this is the most likely value that the variable takes given the structure of the network and the other observed values. In the other cases it is the model component that most likely explains this sample, such as the mixture component that a sample most likely falls under, or the class that is being predicted by a Bayes' classifier.
.. code-block:: python
>>> model.predict_proba(X)
This returns the matrix of posterior probabilities P(M|D) directly. The predict method is simply running argmax over this matrix.
.. code-block:: python
>>> model.predict_log_proba(X)
This returns the matrix of log posterior probabilities for numerical stability.
pomegranate-0.13.5/docs/callbacks.rst 0000664 0000000 0000000 00000010627 13740675601 0017522 0 ustar 00root root 0000000 0000000 .. _callbacks:
Callbacks
=========
- `IPython Notebook Tutorial `_
Callback refer to functions that should be executing during the training procedure. These functions can be executed either at the start of training, the end of each epoch, or at the end of training. They mirror in style the callbacks from keras, and so are passed in using the `callbacks` keyword in `fit` and `from_sample` methods.
In pomegranate, a callback is an object that inherits from the `pomegranate.callbacks.Callback` object and has the following three methods implemented or inherited:
* `on_training_begin(self)` : What should happen when training begins.
* `on_epoch_end(self, logs)` : What should happen at the end of an epoch. The model will pass a dictionary of logs to each callback with each call that includes summary information about the training. The logs file is described more in depth below.
* `on_training_end(self, logs)` : What should happen when training ends. The final set of logs is passed in as well.
The log dictionary that is returned has the following entries:
- `epoch` : `int`, the iteration or epoch that the model is currently on
- `improvement` : `float`, the improvement since the latest iteration in the training set log probability
- `total_improvement` : `float`, the total improvement seen in the training set log probability since the beginning of training
- `log_probability` : `float`, the log probability of the training set after this round of training
- `last_log_probability` : `float`, the log probability of the training set before this round of training
- `duration` : `float`, the time in seconds that this epoch took
- `epoch_start_time` : the time accoding to `time.time()` that this epoch began
- `epoch_end_time`: the time according to `time.time()` that this epoch eded
- `n_seen_batches` : `int`, the number of batches that have been seen by the model, only useful for mini-batching
- `learning_rate` : The learning rate. This is undefined except when a decaying learning rate is set.
The following callbacks are built in to pomegranate:
1. ``History()``: This will keep track of the above values in respective lists, e.g., `history.epochs` and `history.improvements`. This callback is automatically run by all models, and is returned when `return_history=True` is passed in.
.. code-block:: python
from pomegranate.callbacks import History
from pomegranate import *
model = HiddenMarkovModel.from_samples(X) # No history returned
model, history = HiddenMarkovModel.from_samples(X, return_history=True)
2. ``ModelCheckpoint(name=None, verbose=True)``: This callback will save the model parameters to a file named `{name}.{epoch}.json` at the end of each epoch. By default the name is the name of the model, but that can be overriden with the name passed in to the callback object. The verbosity flag indicates if it should print a message to the screen indicating that a file was saved, and where to, at the end of each epoch.
.. code-block:: python
>>> from pomegranate.callbacks import ModelCheckpoint
>>> from pomegranate import *
>>> HiddenMarkovModel.from_samples(X, callbacks=[ModelCheckpoint()])
3. ``CSVLogger(filename, separator=',', append=False)``: This callback will save the statistics from the logs dictionary to rows in a file at the end of each epoch. The filename specifies where to save the logs to, the separator is the symbol to separate values, and append indicates whether to save to the end of a file or to overwrite it, if it currently exists.
.. code-block:: python
>>> from pomegranate.callbacks import CSVLogger, ModelCheckpoint
>>> from pomegranate import *
>>> HiddenMarkovModel.from_samples(X, callbacks=[CSVLogger('model.logs'), ModelCheckpoint()])
4. ``LambdaCallback(on_training_begin=None, on_training_end=None, on_epoch_end=None)``: A convenient wrapper that allows you to pass functions in that get executed at the appropriate points. The function `on_epoch_end` and `on_training_end` should accept a single argument, the dictionary of logs, as described above.
.. code-block:: python
>>> from pomegranate.callbacks import LambdaCheckpoint
>>> from pomegranate import *
>>>
>>> def on_training_end(logs):
>>> print("Total Improvement: {:4.4}".format(logs['total_improvement']))
>>>
>>> HiddenMarkovModel.from_samples(X, callbacks=[LambdaCheckpoint(on_training_end=on_training_end)])
pomegranate-0.13.5/docs/conf.py 0000664 0000000 0000000 00000023341 13740675601 0016345 0 ustar 00root root 0000000 0000000 # -*- coding: utf-8 -*-
#
# pomegranate documentation build configuration file, created by
# sphinx-quickstart on Sun Oct 30 18:10:26 2016.
#
# This file is execfile()d with the current directory set to its
# containing dir.
#
# Note that not all possible configuration values are present in this
# autogenerated file.
#
# All configuration values have a default; values that are commented out
# serve to show the default.
import sys
import os
import subprocess
#import mock
#MOCK_MODULES = ['numpy', 'scipy', 'joblib', 'networkx', 'cython']
#for mod_name in MOCK_MODULES:
# sys.modules[mod_name] = mock.Mock()
subprocess.call('pip install numpydoc', shell=True)
# If extensions (or modules to document with autodoc) are in another directory,
# add these directories to sys.path here. If the directory is relative to the
# documentation root, use os.path.abspath to make it absolute, like shown here.
sys.path.insert(0, os.path.abspath('../..'))
# -- General configuration ------------------------------------------------
# If your documentation needs a minimal Sphinx version, state it here.
#needs_sphinx = '1.0'
# Add any Sphinx extension module names here, as strings. They can be
# extensions coming with Sphinx (named 'sphinx.ext.*') or your custom
# ones.
extensions = [
'sphinx.ext.autodoc',
'sphinx.ext.autosummary',
'sphinx.ext.doctest',
'sphinx.ext.todo',
'sphinx.ext.coverage',
'sphinx.ext.mathjax',
'sphinx.ext.viewcode',
'numpydoc'
]
autosummary_generate = True
numpydoc_show_class_members = False
# Add any paths that contain templates here, relative to this directory.
templates_path = ['_templates']
# The suffix(es) of source filenames.
# You can specify multiple suffix as a list of string:
# source_suffix = ['.rst', '.md']
source_suffix = '.rst'
# The encoding of source files.
#source_encoding = 'utf-8-sig'
# The master toctree document.
master_doc = 'index'
# General information about the project.
project = u'pomegranate'
copyright = u'2016-2018, Jacob Schreiber'
author = u'Jacob Schreiber'
# The version info for the project you're documenting, acts as replacement for
# |version| and |release|, also used in various other places throughout the
# built documents.
#
import pomegranate
# The short X.Y version.
# If you really want the short one use the next line.
# version = '.'.join(pomegranate.__version__.split('.')[0:2])
# Use this version if you want the full version string in the document
version = pomegranate.__version__
# The full version, including alpha/beta/rc tags.
release = pomegranate.__version__
# The language for content autogenerated by Sphinx. Refer to documentation
# for a list of supported languages.
#
# This is also used if you do content translation via gettext catalogs.
# Usually you set "language" from the command line for these cases.
language = None
# There are two options for replacing |today|: either, you set today to some
# non-false value, then it is used:
#today = ''
# Else, today_fmt is used as the format for a strftime call.
#today_fmt = '%B %d, %Y'
# List of patterns, relative to source directory, that match files and
# directories to ignore when looking for source files.
exclude_patterns = ['_build']
# The reST default role (used for this markup: `text`) to use for all
# documents.
#default_role = None
# If true, '()' will be appended to :func: etc. cross-reference text.
#add_function_parentheses = True
# If true, the current module name will be prepended to all description
# unit titles (such as .. function::).
#add_module_names = True
# If true, sectionauthor and moduleauthor directives will be shown in the
# output. They are ignored by default.
#show_authors = False
# The name of the Pygments (syntax highlighting) style to use.
pygments_style = 'sphinx'
# A list of ignored prefixes for module index sorting.
#modindex_common_prefix = []
# If true, keep warnings as "system message" paragraphs in the built documents.
#keep_warnings = False
# If true, `todo` and `todoList` produce output, else they produce nothing.
todo_include_todos = True
# -- Options for HTML output ----------------------------------------------
# The theme to use for HTML and HTML Help pages. See the documentation for
# a list of builtin themes.
html_theme = 'sphinx_rtd_theme'
# Theme options are theme-specific and customize the look and feel of a theme
# further. For a list of options available for each theme, see the
# documentation.
#html_theme_options = {}
# Add any paths that contain custom themes here, relative to this directory.
#html_theme_path = []
# The name for this set of Sphinx documents. If None, it defaults to
# " v documentation".
#html_title = None
# A shorter title for the navigation bar. Default is the same as html_title.
#html_short_title = None
# The name of an image file (relative to this directory) to place at the top
# of the sidebar.
#html_logo = None
# The name of an image file (within the static path) to use as favicon of the
# docs. This file should be a Windows icon file (.ico) being 16x16 or 32x32
# pixels large.
#html_favicon = None
# Add any paths that contain custom static files (such as style sheets) here,
# relative to this directory. They are copied after the builtin static files,
# so a file named "default.css" will overwrite the builtin "default.css".
html_static_path = ['_static']
# Add any extra paths that contain custom files (such as robots.txt or
# .htaccess) here, relative to this directory. These files are copied
# directly to the root of the documentation.
#html_extra_path = []
# If not '', a 'Last updated on:' timestamp is inserted at every page bottom,
# using the given strftime format.
#html_last_updated_fmt = '%b %d, %Y'
# If true, SmartyPants will be used to convert quotes and dashes to
# typographically correct entities.
#html_use_smartypants = True
# Custom sidebar templates, maps document names to template names.
#html_sidebars = {}
# Additional templates that should be rendered to pages, maps page names to
# template names.
#html_additional_pages = {}
# If false, no module index is generated.
#html_domain_indices = True
# If false, no index is generated.
#html_use_index = True
# If true, the index is split into individual pages for each letter.
#html_split_index = False
# If true, links to the reST sources are added to the pages.
#html_show_sourcelink = True
# If true, "Created using Sphinx" is shown in the HTML footer. Default is True.
#html_show_sphinx = True
# If true, "(C) Copyright ..." is shown in the HTML footer. Default is True.
#html_show_copyright = True
# If true, an OpenSearch description file will be output, and all pages will
# contain a tag referring to it. The value of this option must be the
# base URL from which the finished HTML is served.
#html_use_opensearch = ''
# This is the file name suffix for HTML files (e.g. ".xhtml").
#html_file_suffix = None
# Language to be used for generating the HTML full-text search index.
# Sphinx supports the following languages:
# 'da', 'de', 'en', 'es', 'fi', 'fr', 'hu', 'it', 'ja'
# 'nl', 'no', 'pt', 'ro', 'ru', 'sv', 'tr'
#html_search_language = 'en'
# A dictionary with options for the search language support, empty by default.
# Now only 'ja' uses this config value
#html_search_options = {'type': 'default'}
# The name of a javascript file (relative to the configuration directory) that
# implements a search results scorer. If empty, the default will be used.
#html_search_scorer = 'scorer.js'
# Output file base name for HTML help builder.
htmlhelp_basename = 'pomegranatedoc'
# -- Options for LaTeX output ---------------------------------------------
latex_elements = {
# The paper size ('letterpaper' or 'a4paper').
#'papersize': 'letterpaper',
# The font size ('10pt', '11pt' or '12pt').
#'pointsize': '10pt',
# Additional stuff for the LaTeX preamble.
#'preamble': '',
# Latex figure (float) alignment
#'figure_align': 'htbp',
}
# Grouping the document tree into LaTeX files. List of tuples
# (source start file, target name, title,
# author, documentclass [howto, manual, or own class]).
latex_documents = [
(master_doc, 'pomegranate.tex', u'pomegranate Documentation',
u'Jacob Schreiber', 'manual'),
]
# The name of an image file (relative to this directory) to place at the top of
# the title page.
#latex_logo = None
# For "manual" documents, if this is true, then toplevel headings are parts,
# not chapters.
#latex_use_parts = False
# If true, show page references after internal links.
#latex_show_pagerefs = False
# If true, show URL addresses after external links.
#latex_show_urls = False
# Documents to append as an appendix to all manuals.
#latex_appendices = []
# If false, no module index is generated.
#latex_domain_indices = True
# -- Options for manual page output ---------------------------------------
# One entry per manual page. List of tuples
# (source start file, name, description, authors, manual section).
man_pages = [
(master_doc, 'pomegranate', u'pomegranate Documentation',
[author], 1)
]
# If true, show URL addresses after external links.
#man_show_urls = False
# -- Options for Texinfo output -------------------------------------------
# Grouping the document tree into Texinfo files. List of tuples
# (source start file, target name, title, author,
# dir menu entry, description, category)
texinfo_documents = [
(master_doc, 'pomegranate', u'pomegranate Documentation',
author, 'pomegranate', 'One line description of project.',
'Miscellaneous'),
]
# Documents to append as an appendix to all manuals.
#texinfo_appendices = []
# If false, no module index is generated.
#texinfo_domain_indices = True
# How to display URL addresses: 'footnote', 'no', or 'inline'.
#texinfo_show_urls = 'footnote'
# If true, do not generate a @detailmenu in the "Top" node's menu.
#texinfo_no_detailmenu = False
pomegranate-0.13.5/docs/faq.rst 0000664 0000000 0000000 00000020117 13740675601 0016345 0 ustar 00root root 0000000 0000000 .. _faq:
FAQ
===
**Can I create a usable model if I already know the parameters I want, but don't have data to fit to?**
Yes! pomegranate has two ways of initializing models, either by starting off with pre-initialized distributions or by using the ``Model.from_samples`` class method. In the case where you have a model that you'd like to use you can create the model manually and use it to make predictions without the need to fit it to data.
**How do I create a model directly from data?**
pomegranate attempts to closely follow the scikit-learn API. However, a major area in which it diverges is in the initialization of models directly from data. Typically in scikit-learn one would create an estimator and then call the ``fit`` function on the training data. In pomegranate one would use the ``Model.from_samples`` class method, such as ``BayesianNetwork.from_samples(X)``, to learn a model directly from data.
**My data set has missing values. Can I use pomegranate?**
Yes! pomegranate v0.9.0 merged missing value support. This means that you can learn models and run inference on data sets that have missing values just as easily as if they were fully observed. Indicate that a value is missing using either `numpy.nan` for numeric data sets or `'nan'` in string data sets.
**What is the difference between ``fit`` and ``from_samples``?**
The ``fit`` method trains an initialized model, whereas the ``from_samples`` class method will first initialize the model and then train it. These are separated out because frequently a person already knows a good initialization, such as the structure of the Bayesian network but maybe not the parameters, and wants to fine-tune that initialization instead of learning everything directly from data. This also simplifies the backend by allowing the ``fit`` function to assume that the model is initialized instead of having to check to see if it is initialized, and if not then initialize it. This is particularly useful in structured models such as Bayesian networks or hidden Markov models where the ``Model.from_samples`` task is really structure learning + parameter learning, because it allows the ``fit`` function to be solely parameter learning.
**How can I use pomegranate for semi-supervised learning?**
When using one of the supervised models (such as naive Bayes or Bayes classifiers) simply pass in the label -1 for samples that you do not have a label for.
**How can I use out-of-core learning in pomegranate?**
Once a model has been initialized the ``summarize`` method can be used on arbitrarily sized chunks of the data to reduce them into their sufficient statistics. These sufficient statistics are additive, meaning that if they are calculated for all chunks of a dataset and then added together they can yield exact updates. Once all chunks have been summarized then ``from_summaries`` is called to update the parameters of the model based on these added sufficient statistics. Out-of-core computing is supported by allowing the user to load up chunks of data from memory, summarize it, discard it, and move on to the next chunk.
**Does pomegranate support parallelization?**
Yes! pomegranate supports parallelized model fitting and model predictions, both in a data-parallel manner. Since the backend is written in cython the global interpreter lock (GIL) can be released and multi-threaded training can be supported via joblib. This means that parallelization is utilized time isn't spent piping data from one process to another nor are multiple copies of the model made.
**Does pomegranate support GPUs?**
Currently pomegranate does not support GPUs.
**Does pomegranate support distributed computing?**
Currently pomegranate is not set up for a distributed environment, though the pieces are currently there to make this possible.
**How can I cite pomegranate?**
The research paper that presents pomegranate is:
*Schreiber, J. (2018). Pomegranate: fast and flexible probabilistic modeling in python. Journal of Machine Learning Research, 18(164), 1-6.*
which can be downloaded from `JML`_ or from `arXiv`_.
.. _jml: http://www.jmlr.org/papers/volume18/17-636/17-636.pdf
.. _arxiv: https://arxiv.org/abs/1711.00137
The paper can be cited as:
::
@article{schreiber2018pomegranate,
title={Pomegranate: fast and flexible probabilistic modeling in python},
author={Schreiber, Jacob},
journal={Journal of Machine Learning Research},
volume={18},
number={164},
pages={1--6},
year={2018}
}
Alternatively, the GitHub repository can be cited as:
::
@misc{Schreiber2016,
author = {Jacob Schreiber},
title = {pomegranate},
year = {2016},
publisher = {GitHub},
journal = {GitHub repository},
howpublished = {\url{https://github.com/jmschrei/pomegranate}},
commit = {enter commit that you used}
}
**How does pomegranate compare to other packages?**
A comparison of the features between pomegranate and others in the python ecosystem can be seen in the following two plots.
.. image:: logo/pomegranate_comparison.png
The plot on the left shows model stacks which are currently supported by pomegranate. The rows show each model, and the columns show which models those can fit in. Dark blue shows model stacks which currently are supported, and light blue shows model stacks which are currently being worked on and should be available soon. For example, all models use basic distributions as their main component. However, general mixture models (GMMs) can be fit into both Naive Bayes classifiers and hidden Markov models (HMMs). Conversely, HMMs can be fit into GMMs to form mixtures of HMMs. Soon pomegranate will support models like a mixture of Bayesian networks.
The plot on the right shows features compared to other packages in the python ecosystem. Dark red indicates features which no other package supports (to my knowledge!) and orange shows areas where pomegranate has an expanded feature set compared to other packages. For example, both pomegranate and sklearn support Gaussian naive Bayes classifiers. However, pomegranate supports naive Bayes of arbitrary distributions and combinations of distributions, such as one feature being Gaussian, one being log normal, and one being exponential (useful to classify things like ionic current segments or audio segments). pomegranate also extends naive Bayes past its "naivity" to allow for features to be dependent on each other, and allows input to be more complex things like hidden Markov models and Bayesian networks. There's no rule that each of the inputs to naive Bayes has to be the same type though, allowing you to do things like compare a markov chain to a HMM. No other package supports a HMM Naive Bayes! Packages like hmmlearn support the GMM-HMM, but for them GMM strictly means Gaussian mixture model, whereas in pomegranate it ~can~ be a Gaussian mixture model, but it can also be an arbitrary mixture model of any types of distributions. Lastly, no other package supports mixtures of HMMs despite their prominent use in things like audio decoding and biological sequence analysis.
Models can be stacked more than once, though. For example, a "naive" Bayes classifier can be used to compare multiple mixtures of HMMs to each other, or compare a HMM with GMM emissions to one without GMM emissions. You can also create mixtures of HMMs with GMM emissions, and so the most stacking currently supported is a "naive" Bayes classifier of mixtures of HMMs with GMM emissions, or four levels of stacking.
**How can pomegranate be faster than numpy?**
pomegranate has been shown to be faster than numpy at updating univariate and multivariate gaussians. One of the reasons is because when you use numpy you have to use ``numpy.mean(X)`` and ``numpy.cov(X)`` which requires two full passes of the data. pomegranate uses additive sufficient statistics to reduce a dataset down to a fixed set of numbers which can be used to get an exact update. This allows pomegranate to calculate both mean and covariance in a single pass of the dataset. In addition, one of the reasons that numpy is so fast is its use of BLAS. pomegranate also uses BLAS, but uses the cython level calls to BLAS so that the data doesn't have to pass between cython and python multiple times.
pomegranate-0.13.5/docs/gpu.rst 0000664 0000000 0000000 00000003421 13740675601 0016370 0 ustar 00root root 0000000 0000000 .. _gpu:
GPU Usage
=========
pomegranate has GPU accelerated matrix multiplications to speed up all operations involving multivariate Gaussian distributions and all models that use them. This has led to an approximately 4x speedup for multivariate Gaussian mixture models and HMMs compared to using BLAS only. This speedup seems to scale better with dimensionality, with higher dimensional models seeing a larger speedup than smaller dimensional ones.
By default, pomegranate will activate GPU acceleration if it can import cupy, otherwise it will default to BLAS. You can check whether pomegranate is using GPU acceleration with this built-in function:
.. code-block:: python
>>> import pomegranate
>>> print(pomegranate.utils.is_gpu_enabled())
If you'd like to deactivate GPU acceleration you can use the following command:
.. code-block:: python
>>> pomegranate.utils.disable_gpu()
Likewise, if you'd like to activate GPU acceleration you can use the following command:
.. code-block:: python
>>> pomegranate.utils.enable_gpu()
FAQ
---
Q. Why cupy and not Theano?
A. pomegranate only needs to do matrix multiplications using a GPU. While Theano supports an impressive range of more complex operations, it did not have a simple interface to support a matrix-matrix multiplication in the same manner that cupy does.
Q. Why am I not seeing a large speedup with my GPU?
A. There is a cost to transferring data to and from a GPU. It is possible that the GPU isn't fast enough, or that there isn't enough data to utilize the massively parallel aspect of a GPU for your dataset.
Q. Does pomegranate work using my type of GPU?
A. The supported GPUs will be better documented on the cupy package.
Q. Is multi-GPU supported?
A. Currently, no. In theory it should be possible, though.
pomegranate-0.13.5/docs/index.rst 0000664 0000000 0000000 00000007105 13740675601 0016707 0 ustar 00root root 0000000 0000000 .. Introduction documentation master file, created by
sphinx-quickstart on Sun Oct 30 18:10:26 2016.
You can adapt this file completely to your liking, but it should at least
contain the root `toctree` directive.
.. image:: logo/pomegranate-logo.png
:width: 300px
|
.. image:: https://travis-ci.org/jmschrei/pomegranate.svg?branch=master
:target: https://travis-ci.org/jmschrei/pomegranate
.. image:: https://ci.appveyor.com/api/projects/status/github/jmschrei/pomegranate?svg=True
:target: https://ci.appveyor.com/project/JacobSchreiber/pomegranate/branch/master
.. image:: https://readthedocs.org/projects/pomegranate/badge/?version=latest
:target: http://pomegranate.readthedocs.io/en/latest/?badge=latest
|
Home
====
pomegranate is a Python package that implements fast and flexible probabilistic models ranging from individual probability distributions to compositional models such as Bayesian networks and hidden Markov models. The core philosophy behind pomegranate is that all probabilistic models can be viewed as a probability distribution in that they all yield probability estimates for samples and can be updated given samples and their associated weights. The primary consequence of this view is that the components that are implemented in pomegranate can be stacked more flexibly than other packages. For example, one can build a Gaussian mixture model just as easily as building an exponential or log normal mixture model. But that's not all! One can create a Bayes classifier that uses different types of distributions on each features, perhaps modeling time-associated features using an exponential distribution and counts using a Poisson distribution. Lastly, since these compositional models themselves can be viewed as probability distributions, one can build a mixture of Bayesian networks or a hidden Markov model Bayes' classifier that makes predictions over sequences.
In addition to a variety of probability distributions and models, pomegranate has a variety of built-in features that are implemented for all of the models. These include different training strategies such as semi-supervised learning, learning with missing values, and mini-batch learning. It also includes support for massive data supports with out-of-core learning, multi-threaded parallelism, and GPU support.
Thank You
=========
No good project is done alone, and so I'd like to thank all the previous contributors to YAHMM, all the current contributors to pomegranate, and the many graduate students whom I have pestered with ideas and questions.
Contributions
=============
Contributions are eagerly accepted! If you would like to contribute a feature then fork the master branch and be sure to run the tests before changing any code. Let us know what you want to do on the issue tracker just in case we're already working on an implementation of something similar. Also, please don't forget to add tests for any new functions. Please review the `Code of Conduct `_ before contributing.
.. toctree::
:maxdepth: 1
:hidden:
:caption: Getting Started
self
install.rst
CODE_OF_CONDUCT.rst
faq.rst
whats_new.rst
.. toctree::
:maxdepth: 1
:hidden:
:caption: Features
api.rst
ooc.rst
io.rst
semisupervised.rst
parallelism.rst
gpu.rst
nan.rst
callbacks.rst
.. toctree::
:maxdepth: 1
:hidden:
:caption: Models
Distributions.rst
GeneralMixtureModel.rst
HiddenMarkovModel.rst
NaiveBayes.rst
MarkovChain.rst
BayesianNetwork.rst
MarkovNetwork.rst
FactorGraph.rst
pomegranate-0.13.5/docs/install.rst 0000664 0000000 0000000 00000006124 13740675601 0017246 0 ustar 00root root 0000000 0000000 .. _install:
Installation
============
The easiest way to get pomegranate is through pip using the command
.. code-block:: bash
pip install pomegranate
This should install all the dependencies in addition to the package.
You can also get pomegranate through conda using the command
.. code-block:: bash
conda install pomegranate
This version may not be as up to date as the pip version though.
Lastly, you can get the bleeding edge from GitHub using the following commands:
.. code-block:: bash
git clone https://github.com/jmschrei/pomegranate
cd pomegranate
python setup.py install
On Windows machines you may need to download a C++ compiler if you wish to build from source yourself. For Python 2 this `minimal version of Visual Studio 2008 works well `_. For Python 3 `this version of the Visual Studio build tools `_ has been reported to work.
The requirements for pomegranate can be found in the requirements.txt file in the repository, and include numpy, scipy, networkx (v2.0 and above), joblib, cupy (if using a GPU), and cython (if building from source or on an Ubuntu machine).
FAQ
---
Q. I'm on a Windows machine and I'm still encountering problems. What should I do?
A. If those do not work, it has been suggested that https://wiki.python.org/moin/WindowsCompilers may provide more information. Note that your compiler version must fit your python version. Run python --version to tell which python version you use. Don't forget to select the appropriate Windows version API you'd like to use. If you get an error message "ValueError: Unknown MS Compiler version 1900" remove your Python's Lib/distutils/distutil.cfg and retry. See http://stackoverflow.com/questions/34135280/valueerror-unknown-ms-compiler-version-1900 for details.
Q. I've been getting the following error: ```ModuleNotFoundError: No module named 'pomegranate.utils'.```
A. A reported solution is to uninstall and reinstall without cached files using the following:
.. code-block:: bash
pip uninstall pomegranate
pip install pomegranate --no-cache-dir
If that doesn't work for you, you may need to downgrade your version of numpy to 1.11.3 and try the above again.
Q. I've been getting the following error: ```MarkovChain.so: unknown file type, first eight bytes: 0x7F 0x45 0x4C 0x46 0x02 0x01 0x01 0x00.```
A. This can be fixed by removing the .so files from the pomegranate installation or by building pomegranate from source.
Q. I'm encountering some other error when I try to install pomegranate.
A. pomegranate has had some weird linker issues, particularly when users try to upgrade from an older version. In the following order, try:
1. Uninstalling pomegranate using pip and reinstalling it with the option --no-cache-dir, like in the above question.
2. Removing all pomegranate files on your computer manually, including egg and cache files that cython may have left in your site-packages folder
3. Reinstalling the Anaconda distribution (usually only necessary in issues where libgfortran is not linking properly)
pomegranate-0.13.5/docs/io.rst 0000664 0000000 0000000 00000003255 13740675601 0016211 0 ustar 00root root 0000000 0000000 .. _io:
Data Generators and IO
======================
- `IPython Notebook Tutorial `_
The main way that data is fed into most Python machine learning models is formatted as numpy arrays. However, there are some cases where this is not convenient. The first case is when the data doesn't fit into memory. This case was dealt with a little bit in the Out of Core documentation page. The second case is when the data lives in some other format, such as a CSV file or some type of data base, and one doesn't want to create an entire copy of the data formatted as a numpy array.
Fortunately, pomegranate supports the use of data generators as input rather than only taking in numpy arrays. Data generators are objects that wrap data sets and yield batches of data in a manner that is specified by the user. Once the generator is exhausted the epoch is ended. The default data generator is to yield contiguous chunks of examples of a certain batch size until the entire data set has been seen, finish the epoch, and then start over.
The strength of data generators is that they allow the user to have a much greater degree of control over the training process than hardcoding a few training schemes. By specifying how exactly a batch is generated from the data set (and the preprocessing that might go into converting examples for use by the model) and exactly when an epoch ends, users can do a wide variety of out-of-core and mini-batch training schemes without anything needed to be built-in to pomegranate.
See the tutorial for more information about how to use and define your own data generators.
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