gmr
Gaussian Mixture Models (GMMs) for clustering and regression in Python.
.. image:: https://api.travis-ci.org/AlexanderFabisch/gmr.png?branch=master :target: https://travis-ci.org/AlexanderFabisch/gmr :alt: Travis
.. 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>_
New BSD / BSD 3-clause <https://github.com/AlexanderFabisch/gmr/blob/master/LICENSE>_API documentation <https://alexanderfabisch.github.io/gmr/>_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
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/>_.
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.
.. 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>_.
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 is available
here <https://alexanderfabisch.github.io/gmr/>_.
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}
}
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.
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/.
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
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>_.
FAQs
Gaussian Mixture Regression
We found that gmr demonstrated a healthy version release cadence and project activity because the last version was released less than a year ago. It has 3 open source maintainers collaborating on the project.
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