gpflow.posteriors¶

gpflow.posteriors.AbstractPosterior¶

class gpflow.posteriors.AbstractPosterior(kernel, X_data, cache=None, mean_function=None)[source]¶

Bases: gpflow.base.Module, abc.ABC

Attributes

name: Returns the name of this module as passed or determined in the ctor.
name_scope: Returns a tf.name_scope instance for this class.
non_trainable_variables: Sequence of non-trainable variables owned by this module and its submodules.
parameters
submodules: Sequence of all sub-modules.
trainable_parameters
trainable_variables: Sequence of trainable variables owned by this module and its submodules.
variables: Sequence of variables owned by this module and its submodules.

Methods

`fused_predict_f`(Xnew[, full_cov, ...])	Computes predictive mean and (co)variance at Xnew, including mean_function Does not make use of caching
`predict_f`(Xnew[, full_cov, full_output_cov])	Computes predictive mean and (co)variance at Xnew, including mean_function.
`update_cache`([precompute_cache])	Sets the cache depending on the value of precompute_cache to a tf.Tensor, tf.Variable, or clears the cache.
`with_name_scope`(method)	Decorator to automatically enter the module name scope.

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)[source]¶

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

Parameters

Xnew (Union[ndarray, Tensor, Variable, Parameter]) –
full_cov (bool) –
full_output_cov (bool) –

Return type

Tuple[Tensor, Tensor]

predict_f(Xnew, full_cov=False, full_output_cov=False)[source]¶

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

Parameters

Xnew (Union[ndarray, Tensor, Variable, Parameter]) –
full_cov (bool) –
full_output_cov (bool) –

Return type

Tuple[Tensor, Tensor]

update_cache(precompute_cache=None)[source]¶

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)[source]¶

Bases: gpflow.posteriors.AbstractPosterior

Attributes

name: Returns the name of this module as passed or determined in the ctor.
name_scope: Returns a tf.name_scope instance for this class.
non_trainable_variables: Sequence of non-trainable variables owned by this module and its submodules.
parameters
q_mu
q_sqrt
submodules: Sequence of all sub-modules.
trainable_parameters
trainable_variables: Sequence of trainable variables owned by this module and its submodules.
variables: Sequence of variables owned by this module and its submodules.

Methods

`fused_predict_f`(Xnew[, full_cov, ...])	Computes predictive mean and (co)variance at Xnew, including mean_function Does not make use of caching
`predict_f`(Xnew[, full_cov, full_output_cov])	Computes predictive mean and (co)variance at Xnew, including mean_function.
`update_cache`([precompute_cache])	Sets the cache depending on the value of precompute_cache to a tf.Tensor, tf.Variable, or clears the cache.
`with_name_scope`(method)	Decorator to automatically enter the module name scope.

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)[source]¶

Bases: gpflow.posteriors.FullyCorrelatedPosterior

Attributes

name: Returns the name of this module as passed or determined in the ctor.
name_scope: Returns a tf.name_scope instance for this class.
non_trainable_variables: Sequence of non-trainable variables owned by this module and its submodules.
parameters
q_mu
q_sqrt
submodules: Sequence of all sub-modules.
trainable_parameters
trainable_variables: Sequence of trainable variables owned by this module and its submodules.
variables: Sequence of variables owned by this module and its submodules.

Methods

`fused_predict_f`(Xnew[, full_cov, ...])	Computes predictive mean and (co)variance at Xnew, including mean_function Does not make use of caching
`predict_f`(Xnew[, full_cov, full_output_cov])	Computes predictive mean and (co)variance at Xnew, including mean_function.
`update_cache`([precompute_cache])	Sets the cache depending on the value of precompute_cache to a tf.Tensor, tf.Variable, or clears the cache.
`with_name_scope`(method)	Decorator to automatically enter the module name scope.

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)[source]¶

Bases: gpflow.posteriors.BasePosterior

Attributes

name: Returns the name of this module as passed or determined in the ctor.
name_scope: Returns a tf.name_scope instance for this class.
non_trainable_variables: Sequence of non-trainable variables owned by this module and its submodules.
parameters
q_mu
q_sqrt
submodules: Sequence of all sub-modules.
trainable_parameters
trainable_variables: Sequence of trainable variables owned by this module and its submodules.
variables: Sequence of variables owned by this module and its submodules.

Methods

`fused_predict_f`(Xnew[, full_cov, ...])	Computes predictive mean and (co)variance at Xnew, including mean_function Does not make use of caching
`predict_f`(Xnew[, full_cov, full_output_cov])	Computes predictive mean and (co)variance at Xnew, including mean_function.
`update_cache`([precompute_cache])	Sets the cache depending on the value of precompute_cache to a tf.Tensor, tf.Variable, or clears the cache.
`with_name_scope`(method)	Decorator to automatically enter the module name scope.

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_variance, mean_function, *, precompute_cache)[source]¶

Bases: gpflow.posteriors.AbstractPosterior

Attributes

name: Returns the name of this module as passed or determined in the ctor.
name_scope: Returns a tf.name_scope instance for this class.
non_trainable_variables: Sequence of non-trainable variables owned by this module and its submodules.
parameters
submodules: Sequence of all sub-modules.
trainable_parameters
trainable_variables: Sequence of trainable variables owned by this module and its submodules.
variables: Sequence of variables owned by this module and its submodules.

Methods

`fused_predict_f`(Xnew[, full_cov, ...])	Computes predictive mean and (co)variance at Xnew, including mean_function Does not make use of caching
`predict_f`(Xnew[, full_cov, full_output_cov])	Computes predictive mean and (co)variance at Xnew, including mean_function.
`update_cache`([precompute_cache])	Sets the cache depending on the value of precompute_cache to a tf.Tensor, tf.Variable, or clears the cache.
`with_name_scope`(method)	Decorator to automatically enter the module name scope.

Parameters

kernel (Kernel) –
data (Tuple[Union[ndarray, Tensor, Variable, Parameter], Union[ndarray, Tensor, Variable, Parameter]]) –
likelihood_variance (Parameter) –
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)[source]¶

Bases: gpflow.posteriors.BasePosterior

Attributes

name: Returns the name of this module as passed or determined in the ctor.
name_scope: Returns a tf.name_scope instance for this class.
non_trainable_variables: Sequence of non-trainable variables owned by this module and its submodules.
parameters
q_mu
q_sqrt
submodules: Sequence of all sub-modules.
trainable_parameters
trainable_variables: Sequence of trainable variables owned by this module and its submodules.
variables: Sequence of variables owned by this module and its submodules.

Methods

`fused_predict_f`(Xnew[, full_cov, ...])	Computes predictive mean and (co)variance at Xnew, including mean_function Does not make use of caching
`predict_f`(Xnew[, full_cov, full_output_cov])	Computes predictive mean and (co)variance at Xnew, including mean_function.
`update_cache`([precompute_cache])	Sets the cache depending on the value of precompute_cache to a tf.Tensor, tf.Variable, or clears the cache.
`with_name_scope`(method)	Decorator to automatically enter the module name scope.

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)[source]¶

Bases: gpflow.posteriors.IndependentPosterior

Attributes

name: Returns the name of this module as passed or determined in the ctor.
name_scope: Returns a tf.name_scope instance for this class.
non_trainable_variables: Sequence of non-trainable variables owned by this module and its submodules.
parameters
q_mu
q_sqrt
submodules: Sequence of all sub-modules.
trainable_parameters
trainable_variables: Sequence of trainable variables owned by this module and its submodules.
variables: Sequence of variables owned by this module and its submodules.

Methods

`fused_predict_f`(Xnew[, full_cov, ...])	Computes predictive mean and (co)variance at Xnew, including mean_function Does not make use of caching
`predict_f`(Xnew[, full_cov, full_output_cov])	Computes predictive mean and (co)variance at Xnew, including mean_function.
`update_cache`([precompute_cache])	Sets the cache depending on the value of precompute_cache to a tf.Tensor, tf.Variable, or clears the cache.
`with_name_scope`(method)	Decorator to automatically enter the module name scope.

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)[source]¶

Bases: gpflow.posteriors.IndependentPosterior

Attributes

name: Returns the name of this module as passed or determined in the ctor.
name_scope: Returns a tf.name_scope instance for this class.
non_trainable_variables: Sequence of non-trainable variables owned by this module and its submodules.
parameters
q_mu
q_sqrt
submodules: Sequence of all sub-modules.
trainable_parameters
trainable_variables: Sequence of trainable variables owned by this module and its submodules.
variables: Sequence of variables owned by this module and its submodules.

Methods

`fused_predict_f`(Xnew[, full_cov, ...])	Computes predictive mean and (co)variance at Xnew, including mean_function Does not make use of caching
`predict_f`(Xnew[, full_cov, full_output_cov])	Computes predictive mean and (co)variance at Xnew, including mean_function.
`update_cache`([precompute_cache])	Sets the cache depending on the value of precompute_cache to a tf.Tensor, tf.Variable, or clears the cache.
`with_name_scope`(method)	Decorator to automatically enter the module name scope.

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)[source]¶

Bases: gpflow.posteriors.IndependentPosteriorMultiOutput

Attributes

name: Returns the name of this module as passed or determined in the ctor.
name_scope: Returns a tf.name_scope instance for this class.
non_trainable_variables: Sequence of non-trainable variables owned by this module and its submodules.
parameters
q_mu
q_sqrt
submodules: Sequence of all sub-modules.
trainable_parameters
trainable_variables: Sequence of trainable variables owned by this module and its submodules.
variables: Sequence of variables owned by this module and its submodules.

Methods

`fused_predict_f`(Xnew[, full_cov, ...])	Computes predictive mean and (co)variance at Xnew, including mean_function Does not make use of caching
`predict_f`(Xnew[, full_cov, full_output_cov])	Computes predictive mean and (co)variance at Xnew, including mean_function.
`update_cache`([precompute_cache])	Sets the cache depending on the value of precompute_cache to a tf.Tensor, tf.Variable, or clears the cache.
`with_name_scope`(method)	Decorator to automatically enter the module name scope.

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)[source]¶

Bases: enum.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: tensorflow.python.framework.ops.Tensor, axis_dynamic: Tuple[bool, ...])[source]¶

Bases: object

Methods

wrap_alpha_Qinv(alpha, Qinv)

Wraps alpha and Qinv in `PrecomputedValue`s.

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: tensorflow.python.framework.ops.Tensor¶: The precomputed value itself.

static wrap_alpha_Qinv(alpha, Qinv)[source]¶

Wraps alpha and Qinv in `PrecomputedValue`s.

Parameters

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

Return type

Tuple[PrecomputedValue, ...]

gpflow.posteriors.SGPRPosterior¶

class gpflow.posteriors.SGPRPosterior(kernel, data, inducing_variable, likelihood_variance, num_latent_gps, mean_function, *, precompute_cache)[source]¶

Bases: gpflow.posteriors.AbstractPosterior

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

Attributes

name: Returns the name of this module as passed or determined in the ctor.
name_scope: Returns a tf.name_scope instance for this class.
non_trainable_variables: Sequence of non-trainable variables owned by this module and its submodules.
parameters
submodules: Sequence of all sub-modules.
trainable_parameters
trainable_variables: Sequence of trainable variables owned by this module and its submodules.
variables: Sequence of variables owned by this module and its submodules.

Methods

`fused_predict_f`(Xnew[, full_cov, ...])	Computes predictive mean and (co)variance at Xnew, including mean_function Does not make use of caching
`predict_f`(Xnew[, full_cov, full_output_cov])	Computes predictive mean and (co)variance at Xnew, including mean_function.
`update_cache`([precompute_cache])	Sets the cache depending on the value of precompute_cache to a tf.Tensor, tf.Variable, or clears the cache.
`with_name_scope`(method)	Decorator to automatically enter the module name scope.

Parameters

kernel (Kernel) –
data (Tuple[Union[ndarray, Tensor, Variable, Parameter], Union[ndarray, Tensor, Variable, Parameter]]) –
inducing_variable (InducingPoints) –
likelihood_variance (Parameter) –
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)[source]¶

Bases: gpflow.posteriors.AbstractPosterior

Attributes

name: Returns the name of this module as passed or determined in the ctor.
name_scope: Returns a tf.name_scope instance for this class.
non_trainable_variables: Sequence of non-trainable variables owned by this module and its submodules.
parameters
submodules: Sequence of all sub-modules.
trainable_parameters
trainable_variables: Sequence of trainable variables owned by this module and its submodules.
variables: Sequence of variables owned by this module and its submodules.

Methods

`fused_predict_f`(Xnew[, full_cov, ...])	Computes predictive mean and (co)variance at Xnew, including mean_function Does not make use of caching
`predict_f`(Xnew[, full_cov, full_output_cov])	Computes predictive mean and (co)variance at Xnew, including mean_function.
`update_cache`([precompute_cache])	Sets the cache depending on the value of precompute_cache to a tf.Tensor, tf.Variable, or clears the cache.
`with_name_scope`(method)	Decorator to automatically enter the module name scope.

Parameters

kernel (Kernel) –
X (Tensor) –
q_mu (Tensor) –
q_sqrt (Tensor) –
mean_function (Optional[MeanFunction]) –
white (bool) –
precompute_cache (Optional[PrecomputeCacheType]) –

gpflow.posteriors.add_noise_cov¶

gpflow.posteriors.add_noise_cov(K, likelihood_variance)[source]¶

Returns K + σ² I, where σ² is the likelihood noise variance (scalar), and I is the corresponding identity matrix.

Parameters

K (Tensor) –
likelihood_variance (Parameter) –

Return type

Tensor

gpflow.posteriors.base_conditional_with_lm¶

gpflow.posteriors.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.posteriors.create_posterior¶

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

Parameters

kernel (Kernel) –
inducing_variable (InducingVariables) –
q_mu (Union[ndarray, Tensor, Variable, Parameter]) –
q_sqrt (Union[ndarray, Tensor, Variable, Parameter]) –
whiten (bool) –
mean_function (Optional[MeanFunction]) –
precompute_cache (Union[PrecomputeCacheType, str, None]) –

Return type

AbstractPosterior

gpflow.posteriors.expand_independent_outputs¶

gpflow.posteriors.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).
Return type: Tensor
Returns

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

Parameters

full_cov (bool) –
full_output_cov (bool) –

gpflow.posteriors.eye¶

gpflow.posteriors.eye(num, value, dtype=None)[source]¶

Parameters

num (int) –
value (Tensor) –
dtype (Optional[DType]) –

Return type

Tensor

gpflow.posteriors.fully_correlated_conditional¶

gpflow.posteriors.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. :type Kmn: Tensor :param Kmn: [M, N, P] :type Kmm: Tensor :param Kmm: [M, M] :type Knn: Tensor :param Knn: [N, P] or [N, P, N, P] :type f: Tensor :param f: data matrix, [M, 1] :type q_sqrt: Optional[Tensor] :param q_sqrt: [1, M, M] or [1, L] :type full_cov: bool :param full_cov: calculate covariance between inputs :type full_output_cov: bool :param full_output_cov: calculate covariance between outputs :type white: bool :param white: use whitened representation :rtype: Tuple[Tensor, Tensor] :return:

mean: [N, P]

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

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)[source]¶

Parameters

kernel (Kernel) –
inducing_variable (InducingVariables) –

Return type

Type[AbstractPosterior]

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)[source]¶

Parameters

kernel (Kernel) –
inducing_variable (InducingVariables) –

Return type

Type[AbstractPosterior]

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

gpflow.posteriors._get_posterior_independent_mo(kernel, inducing_variable)[source]¶

Parameters

kernel (Kernel) –
inducing_variable (InducingVariables) –

Return type

Type[AbstractPosterior]

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

gpflow.posteriors._get_posterior_independent_mo(kernel, inducing_variable)[source]¶

Parameters

kernel (Kernel) –
inducing_variable (InducingVariables) –

Return type

Type[AbstractPosterior]

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

gpflow.posteriors._get_posterior_independent_mo(kernel, inducing_variable)[source]¶

Parameters

kernel (Kernel) –
inducing_variable (InducingVariables) –

Return type

Type[AbstractPosterior]

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

gpflow.posteriors._get_posterior_independent_mo(kernel, inducing_variable)[source]¶

Parameters

kernel (Kernel) –
inducing_variable (InducingVariables) –

Return type

Type[AbstractPosterior]

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

gpflow.posteriors._get_posterior_independentlatent_mo_fallback(kernel, inducing_variable)[source]¶

Parameters

kernel (Kernel) –
inducing_variable (InducingVariables) –

Return type

Type[AbstractPosterior]

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)[source]¶

Parameters

kernel (Kernel) –
inducing_variable (InducingVariables) –

Return type

Type[AbstractPosterior]

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

gpflow.posteriors._get_posterior_linearcoregionalization_mo_efficient(kernel, inducing_variable)[source]¶

Parameters

kernel (Kernel) –
inducing_variable (InducingVariables) –

Return type

Type[AbstractPosterior]

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)[source]¶

Parameters

kernel (Kernel) –
inducing_variable (InducingVariables) –

Return type

Type[AbstractPosterior]

gpflow.posteriors.independent_interdomain_conditional¶

gpflow.posteriors.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. :type Kmn: Tensor :param Kmn: [M, L, N, P] :type Kmm: Tensor :param Kmm: [L, M, M] :type Knn: Tensor :param Knn: [N, P] or [N, P, P] or [P, N, N] or [N, P, N, P] :type f: Tensor :param f: data matrix, [M, L] :type q_sqrt: Optional[Tensor] :param q_sqrt: [L, M, M] or [M, L] :type full_cov: bool :param full_cov: calculate covariance between inputs :type full_output_cov: bool :param full_output_cov: calculate covariance between outputs :type white: bool :param white: use whitened representation :rtype: Tuple[Tensor, Tensor] :return:

mean: [N, P]

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

gpflow.posteriors.leading_transpose¶

gpflow.posteriors.leading_transpose(tensor, perm, leading_dim=0)[source]¶

Transposes tensors with leading dimensions. Leading dimensions in permutation list represented via ellipsis … and is of type List[Union[int, type(…)] (please note, due to mypy issues, List[Any] is used instead). When leading dimensions are found, transpose method considers them as a single grouped element indexed by 0 in perm list. So, passing perm=[-2, …, -1], you assume that your input tensor has […, A, B] shape, and you want to move leading dims between A and B dimensions. Dimension indices in permutation list can be negative or positive. Valid positive indices start from 1 up to the tensor rank, viewing leading dimensions … as zero index. Example:

a = tf.random.normal((1, 2, 3, 4, 5, 6))
# […, A, B, C], # where A is 1st element, # B is 2nd element and # C is 3rd element in # permutation list, # leading dimensions are [1, 2, 3] # which are 0th element in permutation # list

b = leading_transpose(a, [3, -3, …, -2]) # [C, A, …, B] sess.run(b).shape output> (6, 4, 1, 2, 3, 5)

Parameters

tensor (Tensor) – TensorFlow tensor.
perm (List[Any]) – List of permutation indices.

Return type

Tensor

Returns

TensorFlow tensor.

Raises

ValueError when … cannot be found.

Parameters: leading_dim (int) –

gpflow.posteriors.mix_latent_gp¶

gpflow.posteriors.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)

Return type

Tuple[Tensor, Tensor]

Returns

f_mean and f_var, shape depends on full_cov and full_output_cov

Parameters

full_cov (bool) –
full_output_cov (bool) –

gpflow.posteriors.separate_independent_conditional_implementation¶

gpflow.posteriors.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]

Parameters

Kmns (Tensor) –
Kmms (Tensor) –
Knns (Tensor) –
f (Tensor) –
full_cov (bool) –
q_sqrt (Optional[Tensor]) –
white (bool) –

Return type

Tuple[Tensor, Tensor]