gpflow.models.gpr

Classes

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

$$\log p(Y|{\sigma }_n,\theta )=\mathcal{N}(Y|0,\mathbf{K}+{\sigma }_n^2\mathbf{I})$$

Parameters

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

$$p(F\ast |Y)$$

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

Parameters

• Xnew (Union[ndarray[Any, Any], 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.

Parameters

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

Parameters

precompute_cache (PrecomputeCacheType) –

Return type

GPRPosterior

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[Any, Any], Tensor, Variable, Parameter]) –

• full_cov (bool) –

• full_output_cov (bool) –

Return type

Tuple[Tensor, Tensor]