Multivariate Normal Distribution¶

Module containing expression buildes for the multivariate normal.

breze.arch.component.distributions.mvn.pdf(sample, mean, cov)¶

Return a theano expression representing the values of the probability density function of the multivariate normal.

Parameters:

sample : Theano variable

Array of shape (n, d) where n is the number of samples and d the dimensionality of the data.

mean : Theano variable

Array of shape (d,) representing the mean of the distribution.

cov : Theano variable

Array of shape (d, d) representing the covariance of the distribution.

Returns:

l : Theano variable

Array of shape (n,) where each entry represents the density of the corresponding sample.

Examples

>>> import theano
>>> import theano.tensor as T
>>> import numpy as np
>>> from breze.learn.utils import theano_floatx
>>> sample = T.matrix('sample')
>>> mean = T.vector('mean')
>>> cov = T.matrix('cov')
>>> p = pdf(sample, mean, cov)
>>> f_p = theano.function([sample, mean, cov], p)

>>> mu = np.array([-1, 1])
>>> sigma = np.array([[.9, .4], [.4, .3]])
>>> X = np.array([[-1, 1], [1, -1]])
>>> mu, sigma, X = theano_floatx(mu, sigma, X)
>>> ps = f_p(X, mu, sigma)
>>> np.allclose(ps, [4.798702e-01, 7.73744047e-17])
True

breze.arch.component.distributions.mvn.logpdf(sample, mean, cov)¶

Return a theano expression representing the values of the log probability density function of the multivariate normal.