Orthogonal Gaussian process models

TL;DR

This paper introduces an orthogonal Gaussian process model that improves interpretability by ensuring the stochastic component is orthogonal to the mean, addressing identifiability issues in polynomial mean models, with applications to multi-fidelity simulations.

Contribution

It proposes a novel Gaussian process model with orthogonal components to enhance interpretability and address identifiability issues in polynomial mean models.

Findings

Improved mean model interpretability.

Effective application to multi-fidelity simulations.

Addresses identifiability issues in Gaussian processes.

Abstract

Gaussian processes models are widely adopted for nonparameteric/semi-parametric modeling. Identifiability issues occur when the mean model contains polynomials with unknown coefficients. Though resulting prediction is unaffected, this leads to poor estimation of the coefficients in the mean model, and thus the estimated mean model loses interpretability. This paper introduces a new Gaussian process model whose stochastic part is orthogonal to the mean part to address this issue. This paper also discusses applications to multi-fidelity simulations using data examples.