Fast Gaussian Process Posterior Mean Prediction via Local Cross Validation and Precomputation

TL;DR

This paper introduces FastMuyGPs, a scalable and fast Gaussian process prediction method that combines cross-validation, batching, and precomputation to improve efficiency while maintaining high accuracy on large datasets.

Contribution

The paper presents a novel GP prediction algorithm that significantly reduces computational costs using a combination of techniques, outperforming existing scalable GP methods.

Findings

FastMuyGPs achieves higher accuracy than competing methods.

It offers faster prediction times compared to traditional GPs and neural networks.

The approach scales effectively to large datasets.

Abstract

Gaussian processes (GPs) are Bayesian non-parametric models useful in a myriad of applications. Despite their popularity, the cost of GP predictions (quadratic storage and cubic complexity with respect to the number of training points) remains a hurdle in applying GPs to large data. We present a fast posterior mean prediction algorithm called FastMuyGPs to address this shortcoming. FastMuyGPs is based upon the MuyGPs hyperparameter estimation algorithm and utilizes a combination of leave-one-out cross-validation, batching, nearest neighbors sparsification, and precomputation to provide scalable, fast GP prediction. We demonstrate several benchmarks wherein FastMuyGPs prediction attains superior accuracy and competitive or superior runtime to both deep neural networks and state-of-the-art scalable GP algorithms.