gpflow.models.gpr

gpflow.models.gpr.GPR_deprecated

class gpflow.models.gpr.GPR_deprecated(data, kernel, mean_function=None, noise_variance=1.0)

Bases: gpflow.models.model.GPModel, gpflow.models.training_mixins.InternalDataTrainingLossMixin

Gaussian Process Regression.

This is a vanilla implementation of GP regression with a Gaussian likelihood. Multiple columns of Y are treated independently.

The log likelihood of this model is given by

\[\log p(Y \,|\, \mathbf f) = \mathcal N(Y \,|\, 0, \sigma_n^2 \mathbf{I})\]

To train the model, we maximise the log _marginal_ likelihood w.r.t. the likelihood variance and kernel hyperparameters theta. The marginal likelihood is found by integrating the likelihood over the prior, and has the form

\[\log p(Y \,|\, \sigma_n, \theta) = \mathcal N(Y \,|\, 0, \mathbf{K} + \sigma_n^2 \mathbf{I})\]

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

calc_num_latent_gps(kernel, likelihood, ...)	Calculates the number of latent GPs required given the number of outputs output_dim and the type of likelihood and kernel.
calc_num_latent_gps_from_data(data, kernel, ...)	Calculates the number of latent GPs required based on the data as well as the type of kernel and likelihood.
log_marginal_likelihood()	Computes the log marginal likelihood.
log_posterior_density(*args, **kwargs)	This may be the posterior with respect to the hyperparameters (e.g.
log_prior_density()	Sum of the log prior probability densities of all (constrained) variables in this model.
maximum_log_likelihood_objective()	Objective for maximum likelihood estimation.
predict_f(Xnew[, full_cov, full_output_cov])	This method computes predictions at X in R^{N x D} input points
predict_f_samples(Xnew[, num_samples, ...])	Produce samples from the posterior latent function(s) at the input points.
predict_log_density(data[, full_cov, ...])	Compute the log density of the data at the new data points.
predict_y(Xnew[, full_cov, full_output_cov])	Compute the mean and variance of the held-out data at the input points.
training_loss()	Returns the training loss for this model.
training_loss_closure(*[, compile])	Convenience method.
with_name_scope(method)	Decorator to automatically enter the module name scope.

Parameters

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

• kernel (Kernel) –

• mean_function (Optional[MeanFunction]) –

• noise_variance (float) –

log_marginal_likelihood()

Computes the log marginal likelihood.

\[\log p(Y | \theta).\]

Return type

Tensor

maximum_log_likelihood_objective()

Objective for maximum likelihood estimation. Should be maximized. E.g. log-marginal likelihood (hyperparameter likelihood) for GPR, or lower bound to the log-marginal likelihood (ELBO) for sparse and variational GPs.

Return type

Tensor

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

This method computes predictions at X in R^{N x D} input points

\[p(F* | Y)\]

where F* are points on the GP at new data points, Y are noisy observations at training data points.

Parameters

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

• full_cov (bool) –

• full_output_cov (bool) –

Return type

Tuple[Tensor, Tensor]

gpflow.models.gpr.GPR_with_posterior

class gpflow.models.gpr.GPR_with_posterior(data, kernel, mean_function=None, noise_variance=1.0)

Bases: gpflow.models.gpr.GPR_deprecated

This is an implementation of GPR that provides a posterior() method that enables caching for faster subsequent predictions.

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

calc_num_latent_gps(kernel, likelihood, ...)	Calculates the number of latent GPs required given the number of outputs output_dim and the type of likelihood and kernel.
calc_num_latent_gps_from_data(data, kernel, ...)	Calculates the number of latent GPs required based on the data as well as the type of kernel and likelihood.
log_marginal_likelihood()	Computes the log marginal likelihood.
log_posterior_density(*args, **kwargs)	This may be the posterior with respect to the hyperparameters (e.g.
log_prior_density()	Sum of the log prior probability densities of all (constrained) variables in this model.
maximum_log_likelihood_objective()	Objective for maximum likelihood estimation.
posterior([precompute_cache])	Create the Posterior object which contains precomputed matrices for faster prediction.
predict_f(Xnew[, full_cov, full_output_cov])	For backwards compatibility, GPR's predict_f uses the fused (no-cache) computation, which is more efficient during training.
predict_f_samples(Xnew[, num_samples, ...])	Produce samples from the posterior latent function(s) at the input points.
predict_log_density(data[, full_cov, ...])	Compute the log density of the data at the new data points.
predict_y(Xnew[, full_cov, full_output_cov])	Compute the mean and variance of the held-out data at the input points.
training_loss()	Returns the training loss for this model.
training_loss_closure(*[, compile])	Convenience method.
with_name_scope(method)	Decorator to automatically enter the module name scope.

Parameters

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

• kernel (Kernel) –

• mean_function (Optional[MeanFunction]) –

• noise_variance (float) –

posterior(precompute_cache=PrecomputeCacheType.TENSOR)

Create the Posterior object which contains precomputed matrices for faster prediction.

precompute_cache has three settings:

• 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.

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

For backwards compatibility, GPR’s predict_f uses the fused (no-cache) computation, which is more efficient during training.

For faster (cached) prediction, predict directly from the posterior object, i.e.,:

model.posterior().predict_f(Xnew, …)

Parameters

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

Return type

Tuple[Tensor, Tensor]

gpflow.models.gpr.data_input_to_tensor

gpflow.models.gpr.data_input_to_tensor(structure)

Converts non-tensor elements of a structure to TensorFlow tensors retaining the structure itself. The function doesn’t keep original element’s dtype and forcefully converts them to GPflow’s default float type.