Exact Inference for Gaussian Process Regression in case of Big Data with the Cartesian Product Structure

TL;DR

This paper introduces a novel method for exact Gaussian Process regression tailored for large, multidimensional factorial design datasets, enabling efficient and precise inference despite high computational demands.

Contribution

The paper presents a new algorithm that efficiently performs exact Gaussian Process inference on large, structured datasets with Cartesian product design, improving computational feasibility.

Findings

Enables exact inference on large datasets with Cartesian product structure

Handles anisotropic data effectively

Provides fast and accurate Gaussian Process approximation

Abstract

Approximation algorithms are widely used in many engineering problems. To obtain a data set for approximation a factorial design of experiments is often used. In such case the size of the data set can be very large. Therefore, one of the most popular algorithms for approximation - Gaussian Process regression - can be hardly applied due to its computational complexity. In this paper a new approach for Gaussian Process regression in case of factorial design of experiments is proposed. It allows to efficiently compute exact inference and handle large multidimensional data sets. The proposed algorithm provides fast and accurate approximation and also handles anisotropic data.