COMPUTATIONAL IMPLEMENTATION OF GAUSSIAN PROCESS MODELS

摘要

A computer-implemented method of processing training data comprising a plurality of training data items to determine parameters of a Gaussian process (GP) model comprising a variational Gaussian process (VGP) corresponding to a GP prior conditioned and marginalised with respect to a set of randomly-distributed inducing variables. The method includes initialising first parameters of the VGP including a positive-definite matrix-valued slack parameter, and iteratively modifying the first parameters to increase or decrease an objective function comprising an expected log-likelihood for each training data item under a respective Gaussian distribution with a predictive variance depending on the slack parameter. At an optimal value of the slack parameter, the slack parameter is equal to an inverse of a covariance matrix for the set of inducing variables, and the objective function corresponds to a variational lower bound of a marginal log-likelihood for a posterior distribution corresponding to the GP prior conditioned on the training data.