Wasserstein-Splitting Gaussian Process Regression for Heterogeneous Online Bayesian Inference

TL;DR

This paper introduces a novel online Bayesian inference method using Wasserstein-splitting Gaussian processes, enabling scalable, adaptive, and heterogeneous data modeling through local GP instantiations and ensemble updates.

Contribution

It proposes a Wasserstein-based local splitting strategy combined with variational inference for scalable, adaptive Gaussian process regression in non-stationary, heterogeneous data environments.

Findings

Enables incremental updates of sparse GPs.

Adapts to local data heterogeneity and non-stationarity.

Improves scalability for large datasets.

Abstract

Gaussian processes (GPs) are a well-known nonparametric Bayesian inference technique, but they suffer from scalability problems for large sample sizes, and their performance can degrade for non-stationary or spatially heterogeneous data. In this work, we seek to overcome these issues through (i) employing variational free energy approximations of GPs operating in tandem with online expectation propagation steps; and (ii) introducing a local splitting step which instantiates a new GP whenever the posterior distribution changes significantly as quantified by the Wasserstein metric over posterior distributions. Over time, then, this yields an ensemble of sparse GPs which may be updated incrementally, and adapts to locality, heterogeneity, and non-stationarity in training data.