approx {gplite}

Approximations to the posterior of the latent values

Description

Functions for initializing the approximation for the latent values, which can then be passed to gp_init. The supported methods are:

approx_laplace

Laplace's method, that is, based on local second order approximation to the log likelihood. For Gaussian likelihood, this means exact inference (no approximation).

approx_ep

Expectation propagation, EP. Approximates the likelihood by introducing Gaussian pseudo-data so that the posterior marginals match to the so called tilted distributions (leave-one-out posterior times the true likelihood factor) as closely as possible. Typically more accurate than Laplace, but slower.

Usage

approx_laplace(maxiter = 30, tol = 1e-04)

approx_ep(damping = 0.9, quad_order = 11, maxiter = 100)

Arguments

maxiter

Maximum number of iterations in the Laplace/EP iteration.

tol

Convergence tolerance.

damping

Damping factor for EP. Should be between 0 and 1. Smaller values typically lead to more stable iterations, but also increase the number of iterations, and thus make the algorithm slower.

quad_order

Order of the Gauss-Hermite quadrature used to evaluate the required tilted moments in EP.

Value

The approximation object.

References

Rasmussen, C. E. and Williams, C. K. I. (2006). Gaussian processes for machine learning. MIT Press.

Examples

# Basic usage
gp <- gp_init(
  cfs = cf_sexp(),
  lik = lik_bernoulli(),
  method = method_fitc(num_inducing = 100),
  approx = approx_ep()
)