src.models.tsvgp_sites

Module for the t-SVGP models with individual sites per data point.

Module Contents

class t_SVGP_sites(data: gpflow.models.training_mixins.RegressionData, kernel, likelihood, inducing_variable, *, mean_function=None, num_latent_gps: int = 1, lambda_1=None, lambda_2=None, num_latent: Optional[int] = 1)[source]

Bases: gpflow.models.GPModel

Class for the t-SVGP model with sites

  • 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)[source]

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

property lambda_1(self)[source]

first natural parameter

property lambda_2(self)[source]

second natural parameter

get_mean_chol_cov_inducing_posterior(self)[source]

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

natgrad_step(self, lr=0.1)[source]

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

prior_kl(self) → tf.Tensor[source]

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

maximum_log_likelihood_objective(self) → tf.Tensor[source]

The variational lower bound

elbo(self) → tf.Tensor[source]

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