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) –

    • Kmn has shape [M, batch…, N].

  • Lm (Tensor) –

    • Lm has shape [M, M].

  • Knn (Tensor) –

    • Knn has shape [batch…, N, N] if full_cov.

    • Knn has shape [batch…, N] if not full_cov.

  • f (Tensor) –

    • f has shape [M, R].

  • q_sqrt (Optional[Tensor]) –

    • q_sqrt has shape [M_R_or_R_M_M…].

  • full_cov (bool) –

  • white (bool) –

Return type:

Tuple[Tensor, Tensor]

Returns:

  • return[0] has shape [batch…, N, R].

  • return[1] has shape [batch…, N, R] if not full_cov.

  • return[1] has shape [batch…, R, N, N] if full_cov.

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) –

    • fvar has shape [batch…, N, P] if not full_cov.

    • fvar has shape [batch…, P, N, N] if full_cov.

    Single-output covariance.

  • full_cov (bool) –

  • full_output_cov (bool) –

Return type:

Tensor

Returns:

  • return has shape [batch…, N, P, N, P] if full_cov and full_output_cov.

  • return has shape [batch…, N, P, P] if (not full_cov) and full_output_cov.

  • return has shape [batch…, N, P] if (not full_cov) and (not full_output_cov).

  • return has shape [batch…, P, N, N] if full_cov and (not full_output_cov).

Multi-output covariance.

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:

  • full_cov (bool) – calculate covariance between inputs

  • full_output_cov (bool) – calculate covariance between outputs

  • white (bool) – use whitened representation

  • Kmn (Tensor) –

    • Kmn has shape [M, N, P].

  • Kmm (Tensor) –

    • Kmm has shape [M, M].

  • Knn (Tensor) –

    • Knn has shape [N, P, N, P] if full_cov and full_output_cov.

    • Knn has shape [N, P, P] if (not full_cov) and full_output_cov.

    • Knn has shape [N, P] if (not full_cov) and (not full_output_cov).

    • Knn has shape [P, N, N] if full_cov and (not full_output_cov).

  • f (Tensor) –

    • f has shape [M, 1].

  • q_sqrt (Optional[Tensor]) –

    • q_sqrt has shape [_1_L_or_1_M_M…].

Return type:

Tuple[Tensor, Tensor]

Returns:

  • return[0] has shape [N, P].

  • return[1] has shape [N, P, N, P] if full_cov and full_output_cov.

  • return[1] has shape [N, P, P] if (not full_cov) and full_output_cov.

  • return[1] has shape [N, P] if (not full_cov) and (not full_output_cov).

  • return[1] has shape [P, N, N] if full_cov and (not full_output_cov).

mean, variance

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:

  • full_cov (bool) – calculate covariance between inputs

  • full_output_cov (bool) – calculate covariance between outputs

  • white (bool) – use whitened representation

  • Kmn (Tensor) –

    • Kmn has shape [M, N, P].

  • Kmm (Tensor) –

    • Kmm has shape [M, M].

  • Knn (Tensor) –

    • Knn has shape [N, P, N, P] if full_cov and full_output_cov.

    • Knn has shape [N, P, P] if (not full_cov) and full_output_cov.

    • Knn has shape [N, P] if (not full_cov) and (not full_output_cov).

    • Knn has shape [P, N, N] if full_cov and (not full_output_cov).

  • f (Tensor) –

    • f has shape [M, R].

  • q_sqrt (Optional[Tensor]) –

    • q_sqrt has shape [M_R_or_R_M_M…].

Return type:

Tuple[Tensor, Tensor]

Returns:

  • return[0] has shape [R, N, P].

  • return[1] has shape [R, N, P, N, P] if full_cov and full_output_cov.

  • return[1] has shape [R, N, P, P] if (not full_cov) and full_output_cov.

  • return[1] has shape [R, N, P] if (not full_cov) and (not full_output_cov).

  • return[1] has shape [R, P, N, N] if full_cov and (not full_output_cov).

mean, variance

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:

  • full_cov (bool) – calculate covariance between inputs

  • full_output_cov (bool) – calculate covariance between outputs

  • white (bool) – use whitened representation

  • Kmn (Tensor) –

    • Kmn has shape [M, L, N, P].

  • Kmm (Tensor) –

    • Kmm has shape [L, M, M].

  • Knn (Tensor) –

    • Knn has shape [N, P, N, P] if full_cov and full_output_cov.

    • Knn has shape [N, P, P] if (not full_cov) and full_output_cov.

    • Knn has shape [N, P] if (not full_cov) and (not full_output_cov).

    • Knn has shape [P, N, N] if full_cov and (not full_output_cov).

  • f (Tensor) –

    • f has shape [M, L].

  • q_sqrt (Optional[Tensor]) –

    • q_sqrt has shape [M_L_or_L_M_M…].

Return type:

Tuple[Tensor, Tensor]

Returns:

  • return[0] has shape [N, P].

  • return[1] has shape [N, P, N, P] if full_cov and full_output_cov.

  • return[1] has shape [N, P, P] if (not full_cov) and full_output_cov.

  • return[1] has shape [N, P] if (not full_cov) and (not full_output_cov).

  • return[1] has shape [P, N, N] if full_cov and (not full_output_cov).

mean, variance

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.

Return type:

Tuple[Tensor, Tensor]

Returns:

  • return[0] has shape [batch…, N, P].

  • return[1] has shape [batch…, N, P, N, P] if full_cov and full_output_cov.

  • return[1] has shape [batch…, N, P, P] if (not full_cov) and full_output_cov.

  • return[1] has shape [batch…, N, P] if (not full_cov) and (not full_output_cov).

  • return[1] has shape [batch…, P, N, N] if full_cov and (not full_output_cov).

f_mean and f_var

Parameters:

  • W (Tensor) –

    • W has shape [P, L].

  • g_mean (Tensor) –

    • g_mean has shape [batch…, N, L].

  • g_var (Tensor) –

    • g_var has shape [L, batch…, N, N] if full_cov.

    • g_var has shape [batch…, N, L] if not full_cov.

  • full_cov (bool) –

  • full_output_cov (bool) –

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) –

    • A has shape [left…, right…].

  • num_rolls (int) –

Return type:

Tensor

Returns:

  • return has shape [right…, left…].

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) –

    • A has shape [left…, right…].

  • num_rolls (int) –

Return type:

Tensor

Returns:

  • return has shape [right…, left…].

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.

Return type:

Tensor

Returns:

  • return has shape [batch…, N, D] if num_samples is None.

  • return has shape [batch…, S, N, D] if num_samples is not None.

sample from the MVN

Parameters:

  • mean (Tensor) –

    • mean has shape [batch…, N, D].

  • cov (Tensor) –

    • cov has shape [batch…, N, D, D] if full_cov.

    • cov has shape [batch…, N, D] if not full_cov.

  • full_cov (bool) –

  • num_samples (Optional[int]) –

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).

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) –

    • Kmns has shape [P, M, batch…, N].

  • Kmms (Tensor) –

    • Kmms has shape [P, M, M].

  • Knns (Tensor) –

    • Knns has shape [P, batch…, N, N] if full_cov.

    • Knns has shape [P, batch…, N] if not full_cov.

  • f (Tensor) –

    • f has shape [M, P].

  • q_sqrt (Optional[Tensor]) –

    • q_sqrt has shape [M_R_or_R_M_M…].

  • full_cov (bool) –

  • white (bool) –

Return type:

Tuple[Tensor, Tensor]

Returns:

  • return[0] has shape [batch…, N, R].

  • return[1] has shape [batch…, N, R] if not full_cov.

  • return[1] has shape [batch…, R, N, N] if full_cov.