Healing Products of Gaussian Processes

TL;DR

This paper introduces calibrated and Wasserstein barycenter-based product-of-expert models for Gaussian processes, improving prediction stability and uncertainty quantification in distributed GP systems.

Contribution

It proposes a calibration method using tempered softmax and introduces a novel Wasserstein barycenter approach for combining local GP experts.

Findings

Calibration improves prediction stability and uncertainty estimates.

Wasserstein barycenter method enhances combination of local experts.

Models perform well on regression and classification tasks.

Abstract

Gaussian processes (GPs) are nonparametric Bayesian models that have been applied to regression and classification problems. One of the approaches to alleviate their cubic training cost is the use of local GP experts trained on subsets of the data. In particular, product-of-expert models combine the predictive distributions of local experts through a tractable product operation. While these expert models allow for massively distributed computation, their predictions typically suffer from erratic behaviour of the mean or uncalibrated uncertainty quantification. By calibrating predictions via a tempered softmax weighting, we provide a solution to these problems for multiple product-of-expert models, including the generalised product of experts and the robust Bayesian committee machine. Furthermore, we leverage the optimal transport literature and propose a new product-of-expert model that combines predictions of local experts by computing their Wasserstein barycenter, which can be applied to both regression and classification.