src.models.tsvgp

Module for the t-SVGP model

Module Contents

class base_SVGP(kernel, likelihood, inducing_variable, *, mean_function=None, num_latent_gps: int = 1, num_data=None)

Bases: gpflow.models.model.GPModel, gpflow.models.training_mixins.ExternalDataTrainingLossMixin, abc.ABC

Modified gpflow.svgp.SVGP class to accommodate for different paramaterization of q(u)

• kernel, likelihood, inducing_variables, mean_function are appropriate GPflow objects

• num_latent_gps is the number of latent processes to use, defaults to 1

• num_data is the total number of observations, defaults to X.shape[0] (relevant when feeding in external minibatches)

abstract get_mean_chol_cov_inducing_posterior(self)

Returns the mean and cholesky factor of the covariance matrix of q(u)

prior_kl(self) → tf.Tensor

Returns the KL divergence KL[q(u)|p(u)]

maximum_log_likelihood_objective(self, data: gpflow.models.model.RegressionData) → tf.Tensor

The variational lower bound :param data: input data

elbo(self, data: gpflow.models.model.RegressionData) → tf.Tensor

This gives a variational bound (the evidence lower bound or ELBO) on the log marginal likelihood of the model. :param data: input data

predict_f(self, Xnew: gpflow.models.model.InputData, full_cov=False, full_output_cov=False) → gpflow.models.model.MeanAndVariance

Posterior prediction at new input Xnew :param Xnew: N x D Tensor

class t_SVGP(kernel, likelihood, inducing_variable, *, mean_function=None, num_latent_gps: int = 1, lambda_1=None, lambda_2_sqrt=None, num_data=None, force=False)

Bases: base_SVGP

Class for the t-SVGP model

• kernel, likelihood, inducing_variables, mean_function are appropriate GPflow objects

• num_latent_gps is the number of latent processes to use, defaults to 1

• q_diag is a boolean. If True, the covariance is approximated by a diagonal matrix.

• whiten is a boolean. If True, we use the whitened representation of the inducing points.

• num_data is the total number of observations, defaults to X.shape[0] (relevant when feeding in external minibatches)

_init_variational_parameters(self, num_inducing, lambda_1, lambda_2_sqrt, **kwargs)

Constructs the site parameters λ₁, Λ₂. for site t(u) = exp(uᵀλ₁ - ½ uᵀΛ₂u)

Parameters

• num_inducing – int Number of inducing variables, typically referred to as M.

• lambda_1 – np.array or None First order natural parameter of the variational site.

• lambda_2_sqrt – np.array or None Second order natural parameter of the variational site.

property lambda_1(self)

first natural parameter

property lambda_2_sqrt(self)

Cholesky factor of the second natural parameter

property lambda_2(self)

second natural parameter

get_mean_chol_cov_inducing_posterior(self)

Computes the mean and cholesky factor of the posterior on the inducing variables q(u) = 𝓝(u; m, S) S = (K⁻¹ + Λ₂)⁻¹ = (K⁻¹ + L₂L₂ᵀ)⁻¹ = K - KL₂W⁻¹L₂ᵀK , W = (I + L₂ᵀKL₂)⁻¹ m = S λ₁

new_predict_f(self, Xnew: gpflow.models.model.InputData, full_cov=False, full_output_cov=False) → gpflow.models.model.MeanAndVariance

Posterior prediction at new input Xnew :param Xnew: N x D Tensor

natgrad_step(self, data, lr=0.1, jitter=1e-09)

Takes natural gradient step in Variational parameters in the local parameters λₜ = rₜ▽[Var_exp] + (1-rₜ)λₜ₋₁ Input: :param: X : N x D :param: Y: N x 1 :param: lr: Scalar

Output: Updates the params