gpflow.posteriors

Classes

gpflow.posteriors.AbstractPosterior

class gpflow.posteriors.AbstractPosterior(kernel, X_data, cache=None, mean_function=None)

Bases: Module, ABC

Parameters:

• kernel (Kernel) –

• X_data (Union[Tensor, InducingVariables]) –

• cache (Optional[Tuple[Tensor, ...]]) –

• mean_function (Optional[MeanFunction]) –

fused_predict_f(Xnew, full_cov=False, full_output_cov=False)

Computes predictive mean and (co)variance at Xnew, including mean_function Does not make use of caching

Parameters:

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

  • Xnew has shape [batch…, N, D].

• full_cov (bool) –

• full_output_cov (bool) –

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).

predict_f(Xnew, full_cov=False, full_output_cov=False)

Computes predictive mean and (co)variance at Xnew, including mean_function. Relies on precomputed alpha and Qinv (see _precompute method)

Parameters:

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

  • Xnew has shape [batch…, N, D].

• full_cov (bool) –

• full_output_cov (bool) –

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).

update_cache(precompute_cache=None)

Sets the cache depending on the value of precompute_cache to a tf.Tensor, tf.Variable, or clears the cache. If precompute_cache is not given, the setting defaults to the most-recently-used one.

Parameters:

precompute_cache (Optional[PrecomputeCacheType]) –

Return type:

None

gpflow.posteriors.BasePosterior

class gpflow.posteriors.BasePosterior(kernel, inducing_variable, q_mu, q_sqrt, whiten=True, mean_function=None, *, precompute_cache)

Bases: AbstractPosterior

Parameters:

• kernel (Kernel) –

• inducing_variable (InducingVariables) –

• q_mu (Tensor) –

• q_sqrt (Tensor) –

• whiten (bool) –

• mean_function (Optional[MeanFunction]) –

• precompute_cache (Optional[PrecomputeCacheType]) –

gpflow.posteriors.FallbackIndependentLatentPosterior

class gpflow.posteriors.FallbackIndependentLatentPosterior(kernel, inducing_variable, q_mu, q_sqrt, whiten=True, mean_function=None, *, precompute_cache)

Bases: FullyCorrelatedPosterior

Parameters:

• kernel (Kernel) –

• inducing_variable (InducingVariables) –

• q_mu (Tensor) –

• q_sqrt (Tensor) –

• whiten (bool) –

• mean_function (Optional[MeanFunction]) –

• precompute_cache (Optional[PrecomputeCacheType]) –

gpflow.posteriors.FullyCorrelatedPosterior

class gpflow.posteriors.FullyCorrelatedPosterior(kernel, inducing_variable, q_mu, q_sqrt, whiten=True, mean_function=None, *, precompute_cache)

Bases: BasePosterior

Parameters:

• kernel (Kernel) –

• inducing_variable (InducingVariables) –

• q_mu (Tensor) –

• q_sqrt (Tensor) –

• whiten (bool) –

• mean_function (Optional[MeanFunction]) –

• precompute_cache (Optional[PrecomputeCacheType]) –

gpflow.posteriors.GPRPosterior

class gpflow.posteriors.GPRPosterior(kernel, data, likelihood, mean_function, *, precompute_cache)

Bases: AbstractPosterior

Parameters:

• kernel (Kernel) –

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

• likelihood (Gaussian) –

• mean_function (MeanFunction) –

• precompute_cache (Optional[PrecomputeCacheType]) –

gpflow.posteriors.IndependentPosterior

class gpflow.posteriors.IndependentPosterior(kernel, inducing_variable, q_mu, q_sqrt, whiten=True, mean_function=None, *, precompute_cache)

Bases: BasePosterior

Parameters:

• kernel (Kernel) –

• inducing_variable (InducingVariables) –

• q_mu (Tensor) –

• q_sqrt (Tensor) –

• whiten (bool) –

• mean_function (Optional[MeanFunction]) –

• precompute_cache (Optional[PrecomputeCacheType]) –

gpflow.posteriors.IndependentPosteriorMultiOutput

class gpflow.posteriors.IndependentPosteriorMultiOutput(kernel, inducing_variable, q_mu, q_sqrt, whiten=True, mean_function=None, *, precompute_cache)

Bases: IndependentPosterior

Parameters:

• kernel (Kernel) –

• inducing_variable (InducingVariables) –

• q_mu (Tensor) –

• q_sqrt (Tensor) –

• whiten (bool) –

• mean_function (Optional[MeanFunction]) –

• precompute_cache (Optional[PrecomputeCacheType]) –

gpflow.posteriors.IndependentPosteriorSingleOutput

class gpflow.posteriors.IndependentPosteriorSingleOutput(kernel, inducing_variable, q_mu, q_sqrt, whiten=True, mean_function=None, *, precompute_cache)

Bases: IndependentPosterior

Parameters:

• kernel (Kernel) –

• inducing_variable (InducingVariables) –

• q_mu (Tensor) –

• q_sqrt (Tensor) –

• whiten (bool) –

• mean_function (Optional[MeanFunction]) –

• precompute_cache (Optional[PrecomputeCacheType]) –

gpflow.posteriors.LinearCoregionalizationPosterior

class gpflow.posteriors.LinearCoregionalizationPosterior(kernel, inducing_variable, q_mu, q_sqrt, whiten=True, mean_function=None, *, precompute_cache)

Bases: IndependentPosteriorMultiOutput

Parameters:

• kernel (Kernel) –

• inducing_variable (InducingVariables) –

• q_mu (Tensor) –

• q_sqrt (Tensor) –

• whiten (bool) –

• mean_function (Optional[MeanFunction]) –

• precompute_cache (Optional[PrecomputeCacheType]) –

gpflow.posteriors.PrecomputeCacheType

class gpflow.posteriors.PrecomputeCacheType(value)

Bases: Enum

• PrecomputeCacheType.TENSOR (or “tensor”): Precomputes the cached quantities and stores them as tensors (which allows differentiating through the prediction). This is the default.

• PrecomputeCacheType.VARIABLE (or “variable”): Precomputes the cached quantities and stores them as variables, which allows for updating their values without changing the compute graph (relevant for AOT compilation).

• PrecomputeCacheType.NOCACHE (or “nocache” or None): Avoids immediate cache computation. This is useful for avoiding extraneous computations when you only want to call the posterior’s fused_predict_f method.

gpflow.posteriors.PrecomputedValue

class gpflow.posteriors.PrecomputedValue(value, axis_dynamic)

Bases: object

Parameters:

• value (Tensor) –

• axis_dynamic (Tuple[bool, ...]) –

axis_dynamic: Tuple[bool, ...]

A tuple with one element per dimension of value. That element is True if that dimension of value might change size.

value: Tensor

The precomputed value itself.

static wrap_alpha_Qinv(alpha, Qinv)

Wraps alpha and Qinv in PrecomputedValues.

Parameters:

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

  • alpha has shape [M_L_or_L_M_M…].

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

  • Qinv has shape [M_M_or_L_M_M…].

Return type:

Tuple[PrecomputedValue, ...]

gpflow.posteriors.SGPRPosterior

class gpflow.posteriors.SGPRPosterior(kernel, data, inducing_variable, likelihood, num_latent_gps, mean_function, *, precompute_cache)

Bases: AbstractPosterior

This class represents posteriors which can be derived from SGPR models to compute faster predictions on unseen points.

Parameters:

• kernel (Kernel) –

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

• inducing_variable (InducingPoints) –

• likelihood (Gaussian) –

• num_latent_gps (int) –

• mean_function (MeanFunction) –

• precompute_cache (Optional[PrecomputeCacheType]) –

gpflow.posteriors.VGPPosterior

class gpflow.posteriors.VGPPosterior(kernel, X, q_mu, q_sqrt, mean_function=None, white=True, *, precompute_cache)

Bases: AbstractPosterior

Parameters:

• kernel (Kernel) –

• X (Tensor) –

• q_mu (Tensor) –

• q_sqrt (Tensor) –

• mean_function (Optional[MeanFunction]) –

• white (bool) –

• precompute_cache (Optional[PrecomputeCacheType]) –

Functions

gpflow.posteriors.create_posterior

gpflow.posteriors.create_posterior(kernel, inducing_variable, q_mu, q_sqrt, whiten, mean_function=None, precompute_cache=PrecomputeCacheType.TENSOR)

Parameters:

• kernel (Kernel) –

• inducing_variable (InducingVariables) –

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

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

• whiten (bool) –

• mean_function (Optional[MeanFunction]) –

• precompute_cache (Union[PrecomputeCacheType, str, None]) –

Return type:

BasePosterior

gpflow.posteriors.get_posterior_class

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

gpflow.posteriors.get_posterior_class( Kernel, InducingVariables )
# dispatch to -> gpflow.posteriors._get_posterior_base_case(...)

gpflow.posteriors._get_posterior_base_case(kernel, inducing_variable)

Parameters:

• kernel (Kernel) –

• inducing_variable (InducingVariables) –

Return type:

Type[BasePosterior]

gpflow.posteriors.get_posterior_class( MultioutputKernel, InducingPoints )
# dispatch to -> gpflow.posteriors._get_posterior_fully_correlated_mo(...)

gpflow.posteriors._get_posterior_fully_correlated_mo(kernel, inducing_variable)

Parameters:

• kernel (Kernel) –

• inducing_variable (InducingVariables) –

Return type:

Type[BasePosterior]

gpflow.posteriors.get_posterior_class( SharedIndependent, SeparateIndependentInducingVariables )
gpflow.posteriors.get_posterior_class( SeparateIndependent, SeparateIndependentInducingVariables )
gpflow.posteriors.get_posterior_class( SharedIndependent, SharedIndependentInducingVariables )
gpflow.posteriors.get_posterior_class( SeparateIndependent, SharedIndependentInducingVariables )
# dispatch to -> gpflow.posteriors._get_posterior_independent_mo(...)

gpflow.posteriors._get_posterior_independent_mo(kernel, inducing_variable)

Parameters:

• kernel (Kernel) –

• inducing_variable (InducingVariables) –

Return type:

Type[BasePosterior]

gpflow.posteriors.get_posterior_class( IndependentLatent, FallbackSeparateIndependentInducingVariables )
gpflow.posteriors.get_posterior_class( IndependentLatent, FallbackSharedIndependentInducingVariables )
# dispatch to -> gpflow.posteriors._get_posterior_independentlatent_mo_fallback(...)

gpflow.posteriors._get_posterior_independentlatent_mo_fallback(kernel, inducing_variable)

Parameters:

• kernel (Kernel) –

• inducing_variable (InducingVariables) –

Return type:

Type[BasePosterior]

gpflow.posteriors.get_posterior_class( LinearCoregionalization, SeparateIndependentInducingVariables )
gpflow.posteriors.get_posterior_class( LinearCoregionalization, SharedIndependentInducingVariables )
# dispatch to -> gpflow.posteriors._get_posterior_linearcoregionalization_mo_efficient(...)

gpflow.posteriors._get_posterior_linearcoregionalization_mo_efficient(kernel, inducing_variable)

Parameters:

• kernel (Kernel) –

• inducing_variable (InducingVariables) –

Return type:

Type[BasePosterior]

gpflow.posteriors.get_precomputed_value_shape

gpflow.posteriors.get_precomputed_value_shape(shaped, context)

Parameters:

• shaped (PrecomputedValue) –

• context (ErrorContext) –

Return type:

Optional[Tuple[Optional[int], ...]]