Gaussian process classification using posterior linearisation

TL;DR

This paper introduces a novel Gaussian process classification algorithm called posterior linearisation (PL), which iteratively approximates the posterior with theoretical advantages over expectation propagation, showing improved performance in experiments.

Contribution

The paper presents a new PL algorithm for Gaussian process classification with positive definite covariances and a convergence theorem, outperforming EP in noisy likelihood scenarios.

Findings

PL achieves better accuracy than EP with noisy threshold likelihood.

PL maintains positive definite covariance matrices.

PL demonstrates improved performance in experimental evaluations.

Abstract

This paper proposes a new algorithm for Gaussian process classification based on posterior linearisation (PL). In PL, a Gaussian approximation to the posterior density is obtained iteratively using the best possible linearisation of the conditional mean of the labels and accounting for the linearisation error. PL has some theoretical advantages over expectation propagation (EP): all calculated covariance matrices are positive definite and there is a local convergence theorem. In experimental data, PL has better performance than EP with the noisy threshold likelihood and the parallel implementation of the algorithms.