Gaussian Mixture Regression
Gaussian Mixture Models (GMMs) for clustering and regression in Python.
Source code repository: https://github.com/AlexanderFabisch/gmr
Estimate GMM from samples and sample from GMM:
from gmr import GMM gmm = GMM(n_components=3, random_state=random_state) gmm.from_samples(X) X_sampled = gmm.sample(100)
For more details, see:
Install from PyPI:
sudo pip install gmr
or from source:
sudo python setup.py install
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:
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_]))
Sample from confidence interval
Sample time-invariant trajectories
The first publication that presents the GMR algorithm is
- 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
- 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:
- 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.
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