Structured Variational Inference for Coupled Gaussian Processes

TL;DR

This paper introduces a new variational inference method for coupled Gaussian Processes that efficiently captures posterior dependencies, improving uncertainty estimation in multi-GP models while maintaining scalability.

Contribution

It proposes a novel parameterization of variational posteriors for multiple GPs, enabling scalable inference that captures dependencies beyond mean field approximations.

Findings

Enables fast inference in multi-GP models with dependency structures

Improves posterior uncertainty estimation over mean field methods

Maintains computational efficiency in large-scale settings

Abstract

Sparse variational approximations allow for principled and scalable inference in Gaussian Process (GP) models. In settings where several GPs are part of the generative model, theses GPs are a posteriori coupled. For many applications such as regression where predictive accuracy is the quantity of interest, this coupling is not crucial. Howewer if one is interested in posterior uncertainty, it cannot be ignored. A key element of variational inference schemes is the choice of the approximate posterior parameterization. When the number of latent variables is large, mean field (MF) methods provide fast and accurate posterior means while more structured posterior lead to inference algorithm of greater computational complexity. Here, we extend previous sparse GP approximations and propose a novel parameterization of variational posteriors in the multi-GP setting allowing for fast and scalable inference capturing posterior dependencies.