gpflow.models.gpr#

Classes#

gpflow.models.gpr.GPR_deprecated#

class gpflow.models.gpr.GPR_deprecated(data, kernel, mean_function=None, noise_variance=None, likelihood=None)[source]#

Bases: GPModel, 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

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

For a use example see Basic Usage with GPR.

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 (Union[int, float, Sequence[Any], ndarray[Any, Any], Tensor, Variable, Parameter, None]) –

  • likelihood (Optional[Gaussian]) –

log_marginal_likelihood()[source]#

Computes the log marginal likelihood.

\[\log p(Y | \theta).\]
Return type:

Tensor

Returns:

  • return has shape [].

maximum_log_likelihood_objective()[source]#

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

Returns:

  • return has shape [].

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

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[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).

gpflow.models.gpr.GPR_with_posterior#

class gpflow.models.gpr.GPR_with_posterior(data, kernel, mean_function=None, noise_variance=None, likelihood=None)[source]#

Bases: 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 (Union[int, float, Sequence[Any], ndarray[Any, Any], Tensor, Variable, Parameter, None]) –

  • likelihood (Optional[Gaussian]) –

posterior(precompute_cache=PrecomputeCacheType.TENSOR)[source]#

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)[source]#

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]) –

    • 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).