---

gmr

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Gaussian Mixture Models (GMMs) for clustering and regression in Python.

.. image:: https://codecov.io/gh/AlexanderFabisch/gmr/branch/master/graph/badge.svg?token=R7hSIxb8M2 :target: https://codecov.io/gh/AlexanderFabisch/gmr :alt: Coverage

.. image:: https://joss.theoj.org/papers/10.21105/joss.03054/status.svg :target: https://doi.org/10.21105/joss.03054 :alt: DOI (JOSS)

.. image:: https://zenodo.org/badge/17119390.svg :target: https://zenodo.org/badge/latestdoi/17119390 :alt: DOI (Zenodo)

.. image:: https://raw.githubusercontent.com/AlexanderFabisch/gmr/master/gmr.png

(Source code of example) <https://github.com/AlexanderFabisch/gmr/blob/master/examples/plot_regression.py>_

• Source code repository: https://github.com/AlexanderFabisch/gmr
• License: New BSD / BSD 3-clause <https://github.com/AlexanderFabisch/gmr/blob/master/LICENSE>_
• Releases: https://github.com/AlexanderFabisch/gmr/releases
• API documentation <https://alexanderfabisch.github.io/gmr/>_

Documentation

Installation

Install from PyPI_:

.. code-block:: bash

pip install gmr

If you want to be able to run all examples, pip can install all necessary examples with

.. code-block::

pip install gmr[all]

You can also install gmr from source:

.. code-block:: bash

python setup.py install
# alternatively: pip install -e .

.. _PyPi: https://pypi.python.org/pypi

Example

Estimate GMM from samples, sample from GMM, and make predictions:

.. code-block:: python

import numpy as np
from gmr import GMM

# Your dataset as a NumPy array of shape (n_samples, n_features):
X = np.random.randn(100, 2)

gmm = GMM(n_components=3, random_state=0)
gmm.from_samples(X)

# Estimate GMM with expectation maximization:
X_sampled = gmm.sample(100)

# Make predictions with known values for the first feature:
x1 = np.random.randn(20, 1)
x1_index = [0]
x2_predicted_mean = gmm.predict(x1_index, x1)

For more details, see:

.. code-block:: python

help(gmr)

or have a look at the API documentation <https://alexanderfabisch.github.io/gmr/>_.

How Does It Compare to scikit-learn?

There is an implementation of Gaussian Mixture Models for clustering in scikit-learn <https://scikit-learn.org/stable/modules/classes.html#module-sklearn.mixture>_ as well. Regression could not be easily integrated in the interface of sklearn. That is the reason why I put the code in a separate repository. It is possible to initialize GMR from sklearn though:

.. code-block:: python

from sklearn.mixture import GaussianMixture
from gmr import GMM
gmm_sklearn = GaussianMixture(n_components=3, covariance_type="diag")
gmm_sklearn.fit(X)
gmm = GMM(
    n_components=3, priors=gmm_sklearn.weights_, means=gmm_sklearn.means_,
    covariances=np.array([np.diag(c) for c in gmm_sklearn.covariances_]))

For model selection with sklearn we furthermore provide an optional regressor interface.

Gallery

.. image:: https://raw.githubusercontent.com/AlexanderFabisch/gmr/master/doc/sklearn_initialization.png :width: 60%

Diagonal covariances <https://github.com/AlexanderFabisch/gmr/blob/master/examples/plot_iris_from_sklearn.py>_

.. image:: https://raw.githubusercontent.com/AlexanderFabisch/gmr/master/doc/confidence_sampling.png :width: 60%

Sample from confidence interval <https://github.com/AlexanderFabisch/gmr/blob/master/examples/plot_sample_mvn_confidence_interval.py>_

.. image:: https://raw.githubusercontent.com/AlexanderFabisch/gmr/master/doc/trajectories.png :width: 60%

Generate trajectories <https://github.com/AlexanderFabisch/gmr/blob/master/examples/plot_trajectories.py>_

.. image:: https://raw.githubusercontent.com/AlexanderFabisch/gmr/master/doc/time_invariant_trajectories.png :width: 60%

Sample time-invariant trajectories <https://github.com/AlexanderFabisch/gmr/blob/master/examples/plot_time_invariant_trajectories.py>_

You can find all examples here <https://github.com/AlexanderFabisch/gmr/tree/master/examples>_.

Saving a Model

This library does not directly offer a function to store fitted models. Since the implementation is pure Python, it is possible, however, to use standard Python tools to store Python objects. For example, you can use pickle to temporarily store a GMM:

.. code-block:: python

import numpy as np
import pickle
import gmr
gmm = gmr.GMM(n_components=2)
gmm.from_samples(X=np.random.randn(1000, 3))

# Save object gmm to file 'file'
pickle.dump(gmm, open("file", "wb"))
# Load object from file 'file'
gmm2 = pickle.load(open("file", "rb"))

It might be required to store models more permanently than in a pickle file, which might break with a change of the library or with the Python version. In this case you can choose a storage format that you like and store the attributes gmm.priors, gmm.means, and gmm.covariances. These can be used in the constructor of the GMM class to recreate the object and they can also be used in other libraries that provide a GMM implementation. The MVN class only needs the attributes mean and covariance to define the model.

API Documentation

API documentation is available here <https://alexanderfabisch.github.io/gmr/>_.

Citation

If you use the library gmr in a scientific publication, I would appreciate citation of the following paper:

Fabisch, A., (2021). gmr: Gaussian Mixture Regression. Journal of Open Source Software, 6(62), 3054, https://doi.org/10.21105/joss.03054

Bibtex entry:

.. code-block:: bibtex

@article{Fabisch2021,
doi = {10.21105/joss.03054},
url = {https://doi.org/10.21105/joss.03054},
year = {2021},
publisher = {The Open Journal},
volume = {6},
number = {62},
pages = {3054},
author = {Alexander Fabisch},
title = {gmr: Gaussian Mixture Regression},
journal = {Journal of Open Source Software}
}

Contributing

How can I contribute?

If you discover bugs, have feature requests, or want to improve the documentation, you can open an issue at the issue tracker <https://github.com/AlexanderFabisch/gmr/issues>_ of the project.

If you want to contribute code, please open a pull request via GitHub by forking the project, committing changes to your fork, and then opening a pull request <https://github.com/AlexanderFabisch/gmr/pulls>_ from your forked branch to the main branch of gmr.

Development Environment

I would recommend to install gmr from source in editable mode with pip and install all dependencies:

.. code-block::

pip install -e .[all,test,doc]

You can now run tests with

nosetests --with-coverage

The option --with-coverage will print a coverage report and output an HTML overview to the folder cover/.

Generate Documentation

The API documentation is generated with pdoc3 <https://pdoc3.github.io/pdoc/>_. If you want to regenerate it, you can run

.. code-block:: bash

pdoc gmr --html --skip-errors

Related Publications

The first publication that presents the GMR algorithm is

[1] Z. Ghahramani, M. I. Jordan, "Supervised learning from incomplete data via an EM approach," Advances in Neural Information Processing Systems 6, 1994, pp. 120-127, http://papers.nips.cc/paper/767-supervised-learning-from-incomplete-data-via-an-em-approach

but it does not use the term Gaussian Mixture Regression, which to my knowledge occurs first in

[2] S. Calinon, F. Guenter and A. Billard, "On Learning, Representing, and Generalizing a Task in a Humanoid Robot," in IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), vol. 37, no. 2, 2007, pp. 286-298, doi: `10.1109/TSMCB.2006.886952 <https://doi.org/10.1109/TSMCB.2006.886952>`_.

A recent survey on various regression models including GMR is the following:

[3] F. Stulp, O. Sigaud, "Many regression algorithms, one unified model: A review," in Neural Networks, vol. 69, 2015, pp. 60-79, doi: `10.1016/j.neunet.2015.05.005 <https://doi.org/10.1016/j.neunet.2015.05.005>`_.

Sylvain Calinon has a good introduction in his slides on nonlinear regression <http://calinon.ch/misc/EE613/EE613-slides-9.pdf>_ for his machine learning course <http://calinon.ch/teaching_EPFL.htm>_.