gpflow.conditionals.util#

Functions#

gpflow.conditionals.util.base_conditional_with_lm#

gpflow.conditionals.util.base_conditional_with_lm(Kmn, Lm, Knn, f, *, full_cov=False, q_sqrt=None, white=False)[source]#

Has the same functionality as the base_conditional function, except that instead of Kmm this function accepts Lm, which is the Cholesky decomposition of Kmm.

This allows Lm to be precomputed, which can improve performance.

Parameters

  • Kmn (Tensor) –

  • Lm (Tensor) –

  • Knn (Tensor) –

  • f (Tensor) –

  • full_cov (bool) –

  • q_sqrt (Optional[Tensor]) –

  • white (bool) –

Return type

Tuple[Tensor, Tensor]

gpflow.conditionals.util.expand_independent_outputs#

gpflow.conditionals.util.expand_independent_outputs(fvar, full_cov, full_output_cov)[source]#

Reshapes fvar to the correct shape, specified by full_cov and full_output_cov.

Parameters

  • fvar (Tensor) – has shape [N, P] (full_cov = False) or [P, N, N] (full_cov = True).

  • full_cov (bool) –

  • full_output_cov (bool) –

Return type

Tensor

Returns

  1. full_cov: True and full_output_cov: True fvar [N, P, N, P]

  2. full_cov: True and full_output_cov: False fvar [P, N, N]

  3. full_cov: False and full_output_cov: True fvar [N, P, P]

  4. full_cov: False and full_output_cov: False fvar [N, P]

gpflow.conditionals.util.fully_correlated_conditional#

gpflow.conditionals.util.fully_correlated_conditional(Kmn, Kmm, Knn, f, *, full_cov=False, full_output_cov=False, q_sqrt=None, white=False)[source]#

This function handles conditioning of multi-output GPs in the case where the conditioning points are all fully correlated, in both the prior and posterior.

Parameters

  • Kmn (Tensor) – [M, N, P]

  • Kmm (Tensor) – [M, M]

  • Knn (Tensor) – [N, P] or [N, P, N, P]

  • f (Tensor) – data matrix, [M, 1]

  • q_sqrt (Optional[Tensor]) – [1, M, M] or [1, L]

  • full_cov (bool) – calculate covariance between inputs

  • full_output_cov (bool) – calculate covariance between outputs

  • white (bool) – use whitened representation

Return type

Tuple[Tensor, Tensor]

Returns

  • mean: [N, P]

  • variance: [N, P], [N, P, P], [P, N, N], [N, P, N, P]

gpflow.conditionals.util.fully_correlated_conditional_repeat#

gpflow.conditionals.util.fully_correlated_conditional_repeat(Kmn, Kmm, Knn, f, *, full_cov=False, full_output_cov=False, q_sqrt=None, white=False)[source]#

This function handles conditioning of multi-output GPs in the case where the conditioning points are all fully correlated, in both the prior and posterior. Note: This conditional can handle ‘repetitions’ R, given in f and q_sqrt.

Parameters

  • Kmn (Tensor) – [M, N, P]

  • Kmm (Tensor) – [M, M]

  • Knn (Tensor) – [N, P] or [N, P, P] or [P, N, N] or [N, P, N, P]

  • f (Tensor) – data matrix, [M, R]

  • q_sqrt (Optional[Tensor]) – [R, M, M] or [M, R]

  • full_cov (bool) – calculate covariance between inputs

  • full_output_cov (bool) – calculate covariance between outputs

  • white (bool) – use whitened representation

Return type

Tuple[Tensor, Tensor]

Returns

  • mean: [R, N, P]

  • variance: [R, N, P], [R, N, P, P], [R, P, N, N], [R, N, P, N, P]

gpflow.conditionals.util.independent_interdomain_conditional#

gpflow.conditionals.util.independent_interdomain_conditional(Kmn, Kmm, Knn, f, *, full_cov=False, full_output_cov=False, q_sqrt=None, white=False)[source]#

The inducing outputs live in the g-space (R^L).

Interdomain conditional calculation.

Parameters

  • Kmn (Tensor) – [M, L, N, P]

  • Kmm (Tensor) – [L, M, M]

  • Knn (Tensor) – [N, P] or [N, P, P] or [P, N, N] or [N, P, N, P]

  • f (Tensor) – data matrix, [M, L]

  • q_sqrt (Optional[Tensor]) – [L, M, M] or [M, L]

  • full_cov (bool) – calculate covariance between inputs

  • full_output_cov (bool) – calculate covariance between outputs

  • white (bool) – use whitened representation

Return type

Tuple[Tensor, Tensor]

Returns

  • mean: [N, P]

  • variance: [N, P], [N, P, P], [P, N, N], [N, P, N, P]

gpflow.conditionals.util.mix_latent_gp#

gpflow.conditionals.util.mix_latent_gp(W, g_mean, g_var, full_cov, full_output_cov)[source]#

Takes the mean and variance of an uncorrelated L-dimensional latent GP and returns the mean and the variance of the mixed GP, f = W g, where both f and g are GPs, with W having a shape [P, L]

Parameters

  • W (Tensor) – [P, L]

  • g_mean (Tensor) – […, N, L]

  • g_var (Tensor) – […, N, L] (full_cov = False) or [L, …, N, N] (full_cov = True)

  • full_cov (bool) –

  • full_output_cov (bool) –

Return type

Tuple[Tensor, Tensor]

Returns

f_mean and f_var, shape depends on full_cov and full_output_cov

gpflow.conditionals.util.rollaxis_left#

gpflow.conditionals.util.rollaxis_left(A, num_rolls)[source]#

Roll the tensor A backwards num_rolls times.

Parameters

  • A (Tensor) –

  • num_rolls (int) –

Return type

Tensor

gpflow.conditionals.util.rollaxis_right#

gpflow.conditionals.util.rollaxis_right(A, num_rolls)[source]#

Roll the tensor A forward num_rolls times.

Parameters

  • A (Tensor) –

  • num_rolls (int) –

Return type

Tensor

gpflow.conditionals.util.sample_mvn#

gpflow.conditionals.util.sample_mvn(mean, cov, full_cov, num_samples=None)[source]#

Returns a sample from a D-dimensional Multivariate Normal distribution.

Parameters

  • mean (Tensor) – […, N, D]

  • cov (Tensor) – […, N, D] or […, N, D, D]

  • full_cov (bool) – if True return a “full” covariance matrix, otherwise a “diag”: - “full”: cov holds the full covariance matrix (without jitter) - “diag”: cov holds the diagonal elements of the covariance matrix

  • num_samples (Optional[int]) –

Return type

Tensor

Returns

sample from the MVN of shape […, (S), N, D], S = num_samples

gpflow.conditionals.util.separate_independent_conditional_implementation#

gpflow.conditionals.util.separate_independent_conditional_implementation(Kmns, Kmms, Knns, f, *, full_cov=False, q_sqrt=None, white=False)[source]#

Multi-output GP with independent GP priors.

Number of latent processes equals the number of outputs (L = P). The covariance matrices used to calculate the conditional have the following shape:

  • Kuu: [P, M, M]

  • Kuf: [P, M, N]

  • Kff: [P, N] or [P, N, N]

Further reference:

  • See gpflow.conditionals._conditional for a detailed explanation of conditional in the single-output case.

  • See the multioutput notebook for more information about the multioutput framework.

  • See above for the parameters and the return value.

Parameters

  • Kmns (Tensor) –

  • Kmms (Tensor) –

  • Knns (Tensor) –

  • f (Tensor) –

  • full_cov (bool) –

  • q_sqrt (Optional[Tensor]) –

  • white (bool) –

Return type

Tuple[Tensor, Tensor]