Welcome to pysarpu’s documentation!

pysarpu

PU learning under SAR assumption with unknown propensity. Implementation of the general SAR-EM algorithm.

Free software: MIT license
Documentation: https://pysarpu.readthedocs.io.

Features

TODO

Credits

This package was created with Cookiecutter and the audreyr/cookiecutter-pypackage project template.

Installation

Stable release

To install pysarpu, run this command in your terminal:

$ pip install pysarpu

This is the preferred method to install pysarpu, as it will always install the most recent stable release.

If you don’t have pip installed, this Python installation guide can guide you through the process.

From sources

The sources for pysarpu can be downloaded from the Github repo.

You can either clone the public repository:

$ git clone git://github.com/ocoudray/pysarpu

Or download the tarball:

$ curl -OJL https://github.com/ocoudray/pysarpu/tarball/master

Once you have a copy of the source, you can install it with:

$ python setup.py install

Usage

Import

To use pysarpu in a project:

import pysarpu

PU learning classification model can be imported as follows:

from pysarpu import PU

The definition of a PU model requires the specification of a classification model and of a propensity model. Implementations can be found in sub-modules pysarpu.classification and pysarpu.propensity:

from pysarpu.classification import LinearLogisticRegression, LinearDiscriminantClassifier
from pysarpu.propensity import LogisticPropensity, LogProbitPropensity, GumbelPropensity

Modules

PU learning model

class PUClassifier(cmodel, emodel, da=False)[source]

PU learning classification model under unknown propensity. This model works by specifying a model on the classification and on the propensity and estimates parameters using EM algorithm (SAR-EM, Bekker et al.)

Parameters

cmodel (pysarpu.classification.Classifier) – an instance of class :class: Classifier <pysarpu.classification.Classifier> representing the classification model. This package includes two types of classification models: logistic regression (accessible through pysarpu.classification.LinearLogisticRegression) and linear discriminant analysis (accessible through pysarpu.classification.LinearDiscriminantClassifier)
emodel (pysarpu.propensity.Propensity) – an instance of class pysarpu.propensity.Propensity representing the propensity model. This package includes multiple pre-implemented propensity models: logistic propensity (pysarpu.propensity.LogisticPropensity), log-normal propensity (pysarpu.propensity.LogProbitPropensity) and Gumbel propensity (pysarpu.propensity.GumbelPropensity)
da (bool, optional) – whether the classification model is a discriminant analysis type model (True) or not (False). Indeed, the likelihood maximized is not the same in these two settings. Default: False.

Returns

Return an instance of PU learning model (not yet initialized).

Return type

pysarpu.PUClassifier

initialization(Xc, Xe, Y, w=1.0)[source]

Initialization of parameters for both classification and propensity models before running EM algorithm. The parameters of each models are initialized following their respective method: see initialization methods for cmodel and emodel.

Parameters

Xc (numpy.array of shape $(n,d_1)$) – covariate matrix for classification. The parameters of cmodel will be initialized in agreement with the dimension of the entry data $d_1$.
Xe (numpy.array of shape $(n,d_2)$) – covariate matrix for propensity. The parameters of emodel will be initialized in agreement with the dimension of the entry data $d_2$.
Y (numpy.array vector of size $n$.) – observed labels. Only used in the computation of the initial log-likelihood.

Returns

None

e(Xe)[source]

Propensity function using the current parameters of propensity model emodel.

Parameters: Xe (numpy.array of shape $(n,d_2)$) – covariate matrix for propensity.
Returns: vector of propensity scores.
Return type: numpy.array of size $n$

loge(Xe)[source]

Logarithm of propensity function using the current parameters of propensity model emodel.

Parameters: Xe (numpy.array of shape $(n,d_2)$) – covariate matrix for propensity.
Returns: vector of log-propensity scores.
Return type: numpy.array of size $n$

predict_cproba(Xc)[source]

Class probability predictions using the parameters of the classification model.

Parameters: Xc (numpy.array with shape $(n, d_1)$.) – covariate matrix for classification.
Returns: posterior class probabilities.
Return type: numpy.array vector of size $n$

predict_clogproba(Xc)[source]

Class log-probability predictions using the parameters of the classification model.

Parameters: Xc (numpy.array with shape $(n, d_1)$.) – covariate matrix for classification.
Returns: posterior class log-probabilities.
Return type: numpy.array vector of size $n$

predict_c(Xc, threshold=0.5)[source]

Class binary predictions using the parameters of the classification model.

Parameters

Xc (numpy.array with shape $(n, d_1)$.) – covariate matrix for classification.
threshold (float, optional (in $[0,1]$)) – decision threshold defining the decision rule.

Returns

class predictions.

Return type

numpy.array binary vector of size $n$

predict_proba(Xc, Xe)[source]

Label probability predictions based on the classification model cmodel and the propensity model emodel. Note that this is different from method predict_cproba which returns class probabilities instead.

Parameters

Xc (numpy.array with shape $(n, d_1)$.) – covariate matrix for classification.
Xe (numpy.array with shape $(n, d_2)$.) – covariate matrix for propensity.

Returns

posterior label probabilities.

Return type

numpy.array vector of size $n$

predict_logproba(Xc, Xe)[source]

Label log-probability predictions based on the classification model cmodel and the propensity model emodel. Note that this is different from method predict_clogproba which returns class log-probabilities instead.

Parameters

Xc (numpy.array with shape $(n, d_1)$.) – covariate matrix for classification.
Xe (numpy.array with shape $(n, d_2)$.) – covariate matrix for propensity.

Returns

posterior label log-probabilities.

Return type

numpy.array vector of size $n$

predict(Xc, Xe, threshold=0.5)[source]

Label binary predictions based on the classification model cmodel and the propensity model emodel. Note that this is different from method predict_c which returns class predictions instead.

Parameters

Xc (numpy.array with shape $(n, d_1)$.) – covariate matrix for classification.
Xe (numpy.array with shape $(n, d_2)$.) – covariate matrix for propensity.
threshold (float, optional (in $[0,1]$)) – decision threshold defining the decision rule.

Returns

label binary predictions.

Return type

numpy.array binary vector of size $n$

loglikelihood(Xc, Xe, Y, w=1.0)[source]

Log-likelihood function given the current parameters of classification and propensity models. Note that the funciton returns the mean of individual dlog-likelihoods (instead of the usual sum).

Parameters

Xc (numpy.array with shape $(n, d_1)$.) – covariate matrix for classification.
Xe (numpy.array with shape $(n, d_2)$.) – covariate matrix for propensity.
Y (numpy.array vector of size $n$.) – observed labels. Only used in the computation of the initial log-likelihood.
w (either float (1., default) or numpy.array of size $n$, optional.) – individual weights (experimental, not tested). Apply weights to observations in the computation of the likelihood.

Returns

log-likelihood.

Return type

float

expectation(Xc, Xe, Y)[source]

Compute the expectation step of EM algorithm, return the probabilities for every instance to be of positive class given the observed labels.

Parameters

Xc (numpy.array with shape $(n, d_1)$.) – covariate matrix for classification.
Xe (numpy.array with shape $(n, d_2)$.) – covariate matrix for propensity.
Y (numpy.array vector of size $n$.) – observed labels. Only used in the computation of the initial log-likelihood.

Returns

posterior probabilities

Return type

np.array vector of size $n$

maximisation(Xc, Xe, Y, gamma, w=1.0, warm_start=True, balance=False)[source]

Compute the maximisation step of EM algorithm, update the model parameters in both classification and propensity models.

Parameters

Xc (numpy.array with shape $(n, d_1)$.) – covariate matrix for classification.
Xe (numpy.array with shape $(n, d_2)$.) – covariate matrix for propensity.
Y (numpy.array vector of size $n$.) – observed labels. Only used in the computation of the initial log-likelihood.
gamma (numpy.array of size $n$) – posterior probabilities obtained in the expectation step.
w (either float (1., default) or numpy.array of size $n$, optional.) – individual weights (experimental, not tested). Apply weights to observations in the computation of the likelihood.

Returns

None

fit(Xc, Xe, Y, w=1.0, tol=1e-06, max_iter=10000.0, warm_start=False, balance=False, n_init=20, iter_init=20)[source]

Estimation of PU learning model parameters (classifier and propensity) through EM algorithm. Multiple random initialization are considered and trained over a few iterations. Then, only the one achieving the best log-likelihood is considered and trained until convergence.

Parameters

Xc (numpy.array with shape $(n, d_1)$.) – covariate matrix for classification.
Xe (numpy.array with shape $(n, d_2)$.) – covariate matrix for propensity.
Y (numpy.array vector of size $n$.) – observed labels. Only used in the computation of the initial log-likelihood.
w (either float (1., default) or numpy.array of size $n$, optional.) – individual weights (experimental, not tested). Apply weights to observations in the computation of the likelihood.
tol (float, optional) – tolerance parameter. Once the increase in the log-likelihood is below tol, the algorithm stops (default 1e-6).
max_iter (int, optional) – maximum number of iterations (default: 1e4)
warm_start (bool, optional) – indicates whether current parameters can be used for initialization (True) or if they should be re-initialized before estimation (default False).
balance (bool, optional) – re-balance weights when fitting the propensity model in the maximization (experimental, potentially interesting in highly unbalanced situations). Default: False.
n_init (int, optional) – number of initialization to consider in the Small EM initialization strategy (default: n_init=20)
iter_init (int, optional) – maximum number of iterations to consider for each initialization (default: 20).

Returns

None

save(path)[source]

Saving PU learning model with current parameters as a binary file (rely on pickle library).

Parameters: path (str) – path at which the model should be saved.
Returns: None

Classification models

Two classification models can be found in submodule pysarpu.classification:

a Linear Logistic Regression model
a Linear Discriminant Analysis model

These two models inherit from the general class sklearn.classification.Classifier.

class LinearLogisticRegression[source]

Linear logistic regression model for classification.

Parameters: params (numpy.array vector of size $d_1+1$) – current parameter vector.

initialization(Xc, w=1.0)[source]

Initialization of the parameters of the model. Initial parameters are chosen randomly and the dimension of parameter vector is the dimension of the covariates + 1 (intercept).

Parameters: Xc (numpy.array of shape $(n,d_1)$) – covariate matrix for classification.
Returns: None

fit(Xc, gamma, w=1.0, warm_start=True)[source]

Estimation of the parameters of the model given the covariates and the observed output. Note that the output does not need to be binary classes, it can consist in probability values.

Parameters

Xc (numpy.array of shape $(n,d_1)$) – covariate matrix for classification.
gamma (numpy.array of size $n$) – posterior probabilities obtained in the expectation step.
w (either float (1., default) or numpy.array of size $n$, optional.) – individual weights (experimental, not tested). Apply weights to observations in the computation of the likelihood.
warm_start (bool, optional) – indicates whether current parameters can be used for initialization (True) or if they should be re-initialized before estimation (default False).

Returns

None

eta(Xc)[source]

Class probability predictions given the current parameters.

Parameters: Xc (numpy.array of shape $(n,d_1)$) – covariate matrix for classification.
Returns: class probabilities.
Return type: numpy.array vector of size $n$

logeta(Xc)[source]

Class log-probability predictions given the current parameters.

Parameters: Xc (numpy.array of shape $(n,d_1)$) – covariate matrix for classification.
Returns: class log-probabilities.
Return type: numpy.array vector of size $n$

class LinearDiscriminantClassifier[source]

Linear Discriminant Analysis model for classification.

Parameters: params (dict) – current parameters: pi is the class prior, mu_0 the mean vector for negative class, mu_1 the mean vector for positive class, Sigma the covariance matrix.

initialization(Xc, w=1.0)[source]

Initialization of the parameters of the model:

the class prior pi is randomly and uniformly drawn in $[0,1]$
the mean vectors mu_0 and mu_1 are drawn as standardized gaussian variables
the covariance matrix Sigma is initialized as the empirical covariance matrix of the whole data set.

Parameters: Xc (numpy.array of shape $(n,d_1)$) – covariate matrix for classification.

fit(Xc, gamma, w=1.0, warm_start=True)[source]

Estimation of the parameters of the model given the covariates and the observed output. Note that the output does not need to be binary classes, it can consist in probability values.

Parameters

Xc (numpy.array of shape $(n,d_1)$) – covariate matrix for classification.
gamma (numpy.array of size $n$) – posterior probabilities obtained in the expectation step.
w (either float (1., default) or numpy.array of size $n$, optional.) – individual weights (experimental, not tested). Apply weights to observations in the computation of the likelihood.
warm_start (bool, optional) – indicates whether current parameters can be used for initialization (True) or if they should be re-initialized before estimation (default False). Not important here as the maximization is straightforward and does not depend on the initialization.

Returns

None

eta(Xc)[source]

Class probability predictions given the current parameters.

Parameters: Xc (numpy.array of shape $(n,d_1)$) – covariate matrix for classification.
Returns: class probabilities.
Return type: numpy.array vector of size $n$

logeta(Xc)[source]

Class log-probability predictions given the current parameters.

Parameters: Xc (numpy.array of shape $(n,d_1)$) – covariate matrix for classification.
Returns: class log-probabilities.
Return type: numpy.array vector of size $n$

pdf_pos(Xc)[source]

Individual likelihood for the positive distribution $\mathbb{P}(x \vert Z=1)$ and for the current parameters.

Parameters: Xc (numpy.array of shape $(n,d_1)$) – covariate matrix for classification.
Returns: individual likelihood values.
Return type: numpy.array vector of size $n$

pdf_neg(Xc)[source]

Individual likelihood for the positive distribution $\mathbb{P}(x \vert Z=0)$ and for the current parameters.

Parameters: Xc (numpy.array of shape $(n,d_1)$) – covariate matrix for classification.
Returns: individual likelihood values.
Return type: numpy.array vector of size $n$

Propensity models

Three propensity models are provided in submodule pysarpu.propensity:

a Logistic Regression model
a logistic function with log-normal link function
a logistic function with Weibull link function

class LogisticPropensity[source]: Logistic Propensity : the feature vector Xe is assumed to contain an intercept as its first column

class LogProbitPropensity[source]

class GumbelPropensity[source]

Contributing

Contributions are welcome, and they are greatly appreciated! Every little bit helps, and credit will always be given.

You can contribute in many ways:

Types of Contributions

Report Bugs

Report bugs at https://github.com/ocoudray/pysarpu/issues.

If you are reporting a bug, please include:

Your operating system name and version.
Any details about your local setup that might be helpful in troubleshooting.
Detailed steps to reproduce the bug.

Fix Bugs

Look through the GitHub issues for bugs. Anything tagged with “bug” and “help wanted” is open to whoever wants to implement it.

Implement Features

Look through the GitHub issues for features. Anything tagged with “enhancement” and “help wanted” is open to whoever wants to implement it.

Write Documentation

pysarpu could always use more documentation, whether as part of the official pysarpu docs, in docstrings, or even on the web in blog posts, articles, and such.

Submit Feedback

The best way to send feedback is to file an issue at https://github.com/ocoudray/pysarpu/issues.

If you are proposing a feature:

Explain in detail how it would work.
Keep the scope as narrow as possible, to make it easier to implement.
Remember that this is a volunteer-driven project, and that contributions are welcome :)

Get Started!

Ready to contribute? Here’s how to set up pysarpu for local development.

Fork the pysarpu repo on GitHub.

Clone your fork locally:

$ git clone git@github.com:your_name_here/pysarpu.git

Install your local copy into a virtualenv. Assuming you have virtualenvwrapper installed, this is how you set up your fork for local development:
```
$ mkvirtualenv pysarpu
$ cd pysarpu/
$ python setup.py develop
```
Create a branch for local development:
```
$ git checkout -b name-of-your-bugfix-or-feature
```
Now you can make your changes locally.
When you’re done making changes, check that your changes pass flake8 and the tests, including testing other Python versions with tox:
```
$ flake8 pysarpu tests
$ python setup.py test or pytest
$ tox
```
To get flake8 and tox, just pip install them into your virtualenv.

Commit your changes and push your branch to GitHub:

$ git add .
$ git commit -m "Your detailed description of your changes."
$ git push origin name-of-your-bugfix-or-feature

Submit a pull request through the GitHub website.

Pull Request Guidelines

Before you submit a pull request, check that it meets these guidelines:

The pull request should include tests.
If the pull request adds functionality, the docs should be updated. Put your new functionality into a function with a docstring, and add the feature to the list in README.rst.
The pull request should work for Python 3.5, 3.6, 3.7 and 3.8, and for PyPy. Check https://travis-ci.com/ocoudray/pysarpu/pull_requests and make sure that the tests pass for all supported Python versions.

Tips

To run a subset of tests:

$ python -m unittest tests.test_pysarpu

Deploying

A reminder for the maintainers on how to deploy. Make sure all your changes are committed (including an entry in HISTORY.rst). Then run:

$ bump2version patch # possible: major / minor / patch
$ git push
$ git push --tags

Travis will then deploy to PyPI if tests pass.

Credits

Development Lead

Olivier COUDRAY <olivier.coudray.15@polytechnique.org>

Contributors

None yet. Why not be the first?

History

0.1.0 (2022-10-07)

First release on PyPI.

Welcome to pysarpu’s documentation!

pysarpu

Features

Credits

Installation

Stable release

From sources

Usage

Import

Modules

PU learning model

Classification models

Propensity models

Contributing

Types of Contributions

Report Bugs

Fix Bugs

Implement Features

Write Documentation

Submit Feedback

Get Started!

Pull Request Guidelines

Tips

Deploying

Credits

Development Lead

Contributors

History

0.1.0 (2022-10-07)

Indices and tables