hopsy.Gaussian

class hopsy.Gaussian(self, mean=[0, 0], covariance=[[1, 0], [0, 1]], inactives=[])

Gaussian model which can be invariant in some dimensions of the input vector. As an example, consider the one-dimensional squared exponential as a function of two input variables

\[f(x_1, x_2) = \exp\big\{ -x_1^2 \big\}\]

then this function is invariant under the second dimension. We also say, that the second component of the input vector \((x_1, x_2)\) is inactive. The degenerate multivariate Gaussian is defined as a regular Gaussian in \(n-k\) dimensions, where the input vector has \(n\) dimensions but \(k\) of its components are inactive.

Technically, this is realized by removing the rows and columns from the mean vector and covariance matrix, that correspond to the inactive dimensions. This then basically constructs a Gaussian in \(n-k\) dimensions. However, unlike a standard multivariate Gaussian model, this model will still (and only) accept input vectors of dimension \(n\).

Passing an empty list as inactives will define a common multivariate Gaussian.

Parameters:

• mean (numpy.ndarray[n, 1]) – Gaussian mean vector

• covariance (numpy.ndarray[n, n]) – Gaussian covariance matrix

• inactives (list[int]) – List of inactive dimensions, so entries should be between 0 and \(n-1\).

Attributes

covariance	The Gaussian's covariance matrix in full space, thus having \(n^2\) entries.
inactives	List of indices of the inactive dimensions.
mean	The Gaussian's mean vector in full space, having \(n\) entries.

Methods

compute_expected_fisher_information(self, x)	deprecated:: 1.4
compute_log_likelihood_gradient(self, x)	deprecated:: 1.4
compute_negative_log_likelihood(self, x)	deprecated:: 1.4
log_curvature(self x)	Computes the expected fisher information of a multivariate Gaussian model in \(n-k\) dimensions at x.
log_density(self, x)	Computes the probability density function of a multivariate Gaussian model in \(m-k\) dimensions at x.
log_gradient(self, x)	Computes the gradient of the logarithm of the probability density function of a multivariate Gaussian model in \(n-k\) dimensions at x.