# gmr **Repository Path**: mirrors_lepy/gmr ## Basic Information - **Project Name**: gmr - **Description**: Gaussian Mixture Regression - **Primary Language**: Unknown - **License**: BSD-3-Clause - **Default Branch**: master - **Homepage**: None - **GVP Project**: No ## Statistics - **Stars**: 0 - **Forks**: 0 - **Created**: 2021-12-16 - **Last Updated**: 2025-09-06 ## Categories & Tags **Categories**: Uncategorized **Tags**: None ## README *** 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) `_ * Source code repository: https://github.com/AlexanderFabisch/gmr * License: `New BSD / BSD 3-clause `_ * Releases: https://github.com/AlexanderFabisch/gmr/releases * `API documentation `_ 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 `_. How Does It Compare to scikit-learn? ------------------------------------ There is an implementation of Gaussian Mixture Models for clustering in `scikit-learn `_ 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 `_ .. image:: https://raw.githubusercontent.com/AlexanderFabisch/gmr/master/doc/confidence_sampling.png :width: 60% `Sample from confidence interval `_ .. image:: https://raw.githubusercontent.com/AlexanderFabisch/gmr/master/doc/trajectories.png :width: 60% `Generate trajectories `_ .. image:: https://raw.githubusercontent.com/AlexanderFabisch/gmr/master/doc/time_invariant_trajectories.png :width: 60% `Sample time-invariant trajectories `_ You can find `all examples here `_. 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 `_. 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 `_ 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 `_ 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 `_. 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 `_. 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 `_. Sylvain Calinon has a good introduction in his `slides on nonlinear regression `_ for his `machine learning course `_.