gpflow.models.vgp#

Classes#

gpflow.models.vgp.VGP_deprecated#

class gpflow.models.vgp.VGP_deprecated(data, kernel, likelihood, mean_function=None, num_latent_gps=None)[source]#

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

This method approximates the Gaussian process posterior using a multivariate Gaussian.

The idea is that the posterior over the function-value vector F is approximated by a Gaussian, and the KL divergence is minimised between the approximation and the posterior.

This implementation is equivalent to SVGP with X=Z, but is more efficient. The whitened representation is used to aid optimization.

The posterior approximation is

\[q(\mathbf f) = N(\mathbf f \,|\, \boldsymbol \mu, \boldsymbol \Sigma)\]
Parameters

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

  • kernel (Kernel) –

  • likelihood (Likelihood) –

  • mean_function (Optional[MeanFunction]) –

  • num_latent_gps (Optional[int]) –

elbo()[source]#

This method computes the variational lower bound on the likelihood, which is:

E_{q(F)} [ log p(Y|F) ] - KL[ q(F) || p(F)]

with

q(mathbf f) = N(mathbf f ,|, boldsymbol mu, boldsymbol Sigma)

Return type

Tensor

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

gpflow.models.vgp.VGP_with_posterior#

class gpflow.models.vgp.VGP_with_posterior(data, kernel, likelihood, mean_function=None, num_latent_gps=None)[source]#

Bases: gpflow.models.vgp.VGP_deprecated

This is an implementation of VGP 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) –

  • likelihood (Likelihood) –

  • mean_function (Optional[MeanFunction]) –

  • num_latent_gps (Optional[int]) –

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

VGPPosterior

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

For backwards compatibility, VGP’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]

Functions#

gpflow.models.vgp.update_vgp_data#

gpflow.models.vgp.update_vgp_data(vgp, new_data)[source]#

Set the data on the given VGP model, and update its variational parameters.

As opposed to many of the other models the VGP has internal parameters whose shape depends on the shape of the data. This functions updates the internal data of the given vgp, and updates the variational parameters to fit.

This function requires that the input vgp were create with tf.Variable`s for `data.

Parameters
Return type

None