Parallel Gaussian Process Regression with Low-Rank Covariance Matrix Approximations

TL;DR

This paper introduces two parallel Gaussian process regression methods using low-rank covariance matrix approximations, enabling scalable, real-time predictions on large datasets by distributing computation across multiple machines.

Contribution

The paper proposes novel parallel GP regression techniques with theoretical guarantees and empirical validation, improving scalability and efficiency over traditional methods.

Findings

Significantly faster and more scalable than centralized and exact GPs

Achieves predictive performance comparable to full Gaussian processes

Effective on real-world datasets with 20 computing nodes

Abstract

Gaussian processes (GP) are Bayesian non-parametric models that are widely used for probabilistic regression. Unfortunately, it cannot scale well with large data nor perform real-time predictions due to its cubic time cost in the data size. This paper presents two parallel GP regression methods that exploit low-rank covariance matrix approximations for distributing the computational load among parallel machines to achieve time efficiency and scalability. We theoretically guarantee the predictive performances of our proposed parallel GPs to be equivalent to that of some centralized approximate GP regression methods: The computation of their centralized counterparts can be distributed among parallel machines, hence achieving greater time efficiency and scalability. We analytically compare the properties of our parallel GPs such as time, space, and communication complexity. Empirical evaluation on two real-world datasets in a cluster of 20 computing nodes shows that our parallel GPs are significantly more time-efficient and scalable than their centralized counterparts and exact/full GP while achieving predictive performances comparable to full GP.