gpflow.kullback_leiblers#

Functions#

gpflow.kullback_leiblers.gauss_kl#

gpflow.kullback_leiblers.gauss_kl(q_mu, q_sqrt, K=None, *, K_cholesky=None)[source]#

Compute the KL divergence KL[q || p] between:

q(x) = N(q_mu, q_sqrt^2)

and:

p(x) = N(0, K)    if K is not None
p(x) = N(0, I)    if K is None

We assume L multiple independent distributions, given by the columns of q_mu and the first or last dimension of q_sqrt. Returns the sum of the divergences.

q_mu is a matrix ([M, L]), each column contains a mean.

  • q_sqrt can be a 3D tensor ([L, M, M]), each matrix within is a lower triangular square-root matrix of the covariance of q.

  • q_sqrt can be a matrix ([M, L]), each column represents the diagonal of a square-root matrix of the covariance of q.

K is the covariance of p (positive-definite matrix). The K matrix can be passed either directly as K, or as its Cholesky factor, K_cholesky. In either case, it can be a single matrix [M, M], in which case the sum of the L KL divergences is computed by broadcasting, or L different covariances [L, M, M].

Note: if no K matrix is given (both K and K_cholesky are None), gauss_kl computes the KL divergence from p(x) = N(0, I) instead.

Parameters

  • q_mu (Union[ndarray[Any, Any], Tensor, Variable, Parameter]) –

  • q_sqrt (Union[ndarray[Any, Any], Tensor, Variable, Parameter]) –

  • K (Union[ndarray[Any, Any], Tensor, Variable, Parameter, None]) –

  • K_cholesky (Union[ndarray[Any, Any], Tensor, Variable, Parameter, None]) –

Return type

Tensor

gpflow.kullback_leiblers.prior_kl#

This function uses multiple dispatch, which will depend on the type of argument passed in:

gpflow.kullback_leiblers.prior_kl( InducingVariables, Kernel, object, object )
# dispatch to -> gpflow.kullback_leiblers._(...)
gpflow.kullback_leiblers._(inducing_variable, kernel, q_mu, q_sqrt, whiten=False)[source]#
Parameters

  • inducing_variable (InducingVariables) –

  • kernel (Kernel) –

  • q_mu (Union[ndarray[Any, Any], Tensor, Variable, Parameter]) –

  • q_sqrt (Union[ndarray[Any, Any], Tensor, Variable, Parameter]) –

  • whiten (bool) –

Return type

Tensor