gpflux.sampling.utils#

Module Contents#

_cholesky_with_jitter(cov: gpflow.base.TensorType) → tf.Tensor[source]#

Compute the Cholesky of the covariance, adding jitter (determined by gpflow.default_jitter()) to the diagonal to improve stability.

Parameters:

cov – full covariance with shape [..., N, D, D].

draw_conditional_sample(mean: gpflow.base.TensorType, cov: gpflow.base.TensorType, f_old: gpflow.base.TensorType) → tf.Tensor[source]#

Draw a sample ${\tilde{f}}_{\text{new}}$ from the conditional multivariate Gaussian $p(f_{\text{new}}|f_{\text{old}})$, where the parameters mean and cov are the mean and covariance matrix of the joint multivariate Gaussian over $[f_{\text{old}},f_{\text{new}}]$.

Parameters:

• mean –

  A tensor with the shape [..., D, N+M] with the mean of [f_old, f_new]. For each [..., D] this is a stacked vector of the form:

  $$\begin{array}{r}\left(\begin{array}{c}\mathrm{mean}(f_{\text{old}})[N]\\ \mathrm{mean}(f_{\text{new}})[M]\end{array}\right)\end{array}$$

• cov –

  A tensor with the shape [..., D, N+M, N+M] with the covariance of [f_old, f_new]. For each [..., D], there is a 2x2 block matrix of the form:

  $$\begin{array}{r}\left(\begin{array}{cc}\mathrm{cov}(f_{\text{old}},f_{\text{old}})[N,N]& \mathrm{cov}(f_{\text{old}},f_{\text{new}})[N,M]\\ \mathrm{cov}(f_{\text{new}},f_{\text{old}})[M,N]& \mathrm{cov}(f_{\text{new}},f_{\text{new}})[M,M]\end{array}\right)\end{array}$$

• f_old – A tensor of observations with the shape [..., D, N], drawn from Normal distribution with mean $\mathrm{mean}(f_{\text{old}})[N]$, and covariance $\mathrm{cov}(f_{\text{old}},f_{\text{old}})[N,N]$

Returns:

A sample ${\tilde{f}}_{\text{new}}$ from the conditional normal $p(f_{\text{new}}|f_{\text{old}})$ with the shape [..., D, M].