Polynomial Chaos Expanded Gaussian Process

TL;DR

This paper introduces Polynomial Chaos Expanded Gaussian Process (PCEGP), a novel machine learning model that combines polynomial chaos expansion with Gaussian processes to effectively capture both global and local behaviors in complex systems.

Contribution

The study presents a new PCEGP model that uses polynomial chaos to adapt Gaussian process hyperparameters, enabling interpretable, non-stationary, and heteroscedastic modeling with competitive performance.

Findings

PCEGP achieves low prediction errors in benchmark tests.

Model performance is often better than existing methods.

Training and prediction runtimes are comparable to standard GPs.

Abstract

In complex and unknown processes, global models are initially generated over the entire experimental space but often fail to provide accurate predictions in local areas. A common approach is to use local models, which requires partitioning the experimental space and training multiple models, adding significant complexity. Recognizing this limitation, this study addresses the need for models that effectively represent both global and local experimental spaces. It introduces a novel machine learning (ML) approach: Polynomial Chaos Expanded Gaussian Process (PCEGP), leveraging polynomial chaos expansion (PCE) to calculate input-dependent hyperparameters of the Gaussian process (GP). This provides a mathematically interpretable approach that incorporates non-stationary covariance functions and heteroscedastic noise estimation to generate locally adapted models. The model performance is compared to different algorithms in benchmark tests for regression tasks. The results demonstrate low prediction errors of the PCEGP, highlighting model performance that is often competitive with or better than previous methods. A key advantage of the presented model is its interpretable hyperparameters along with training and prediction runtimes comparable to those of a GP.