GaussianMixture initialization using component parameters - sklearn

问题

I want to use sklearn.mixture.GaussianMixture to store a gaussian mixture model so that I can later use it to generate samples or a value at a sample point using score_samples method. Here is an example where the components have the following weight, mean and covariances

import numpy as np
weights = np.array([0.6322941277066596, 0.3677058722933399])
mu = np.array([[0.9148052872961359, 1.9792961751316835], 
               [-1.0917396392992502, -0.9304220945910037]])
sigma = np.array([[[2.267889129267119, 0.6553245618368836], 
                        [0.6553245618368835, 0.6571014653342457]], 
                       [[0.9516607767206848, -0.7445831474157608], 
                        [-0.7445831474157608, 1.006599716443763]]])

Then I initialised the mixture as follow

from sklearn import mixture
gmix = mixture.GaussianMixture(n_components=2, covariance_type='full')
gmix.weights_ = weights   # mixture weights (n_components,) 
gmix.means_ = mu          # mixture means (n_components, 2) 
gmix.covariances_ = sigma  # mixture cov (n_components, 2, 2)

Finally I tried to generate a sample based on the parameters which resulted in an error:

x = gmix.sample(1000)
NotFittedError: This GaussianMixture instance is not fitted yet. Call 'fit' with appropriate arguments before using this method.

As I understand GaussianMixture is intended to fit a sample using a mixture of Gaussian but is there a way to provide it with the final values and continue from there?

回答1:

It seems that it has a check that makes sure that the model has been trained. You could trick it by training the GMM on a very small data set before setting the parameters. Like this:

gmix = mixture.GaussianMixture(n_components=2, covariance_type='full')
gmix.fit(rand(10, 2))  # Now it thinks it is trained
gmix.weights_ = weights   # mixture weights (n_components,) 
gmix.means_ = mu          # mixture means (n_components, 2) 
gmix.covariances_ = sigma  # mixture cov (n_components, 2, 2)
x = gmix.sample(1000)  # Should work now

回答2:

You rock, J.P.Petersen! After seeing your answer I compared the change introduced by using fit method. It seems the initial instantiation does not create all the attributes of gmix. Specifically it is missing the following attributes,

covariances_
means_
weights_
converged_
lower_bound_
n_iter_
precisions_
precisions_cholesky_

The first three are introduced when the given inputs are assigned. Among the rest, for my application the only attribute that I need is precisions_cholesky_ which is cholesky decomposition of the inverse covarinace matrices. As a minimum requirement I added it as follow,

gmix.precisions_cholesky_ = np.linalg.cholesky(np.linalg.inv(sigma)).transpose((0, 2, 1))

回答3:

To understand what is happening, what GaussianMixture first checks that it has been fitted:

self._check_is_fitted()

Which triggers the following check:

def _check_is_fitted(self):
    check_is_fitted(self, ['weights_', 'means_', 'precisions_cholesky_'])

And finally the last function call:

def check_is_fitted(estimator, attributes, msg=None, all_or_any=all):

which only checks that the classifier already has the attributes.

So in short, the only thing you have missing to have it working (without having to fit it) is to set precisions_cholesky_ attribute:

gmix.precisions_cholesky_ = 0

should do the trick (can't try it so not 100% sure :P)

However, if you want to play safe and have a consistent solution in case scikit-learn updates its contrains, the solution of @J.P.Petersen is probably the best way to go.

来源：https://stackoverflow.com/questions/42392887/gaussianmixture-initialization-using-component-parameters-sklearn

标签

python

numpy

scikit-learn

gaussian

mixture