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