Extended T-process Regression Models

TL;DR

This paper introduces an extended t-process regression model that offers robust predictions and handles outliers effectively, inheriting desirable properties from Gaussian process regression while improving robustness.

Contribution

The paper proposes a novel extended t-process regression model that enhances robustness and maintains computational efficiency, with explicit predictive distributions and applicability to high-dimensional data.

Findings

The eTPR model provides robust predictions in the presence of outliers.

Simulation and real data show eTPR outperforms existing methods in robustness and accuracy.

The model retains properties of Gaussian process regression, such as closed-form distributions.

Abstract

Gaussian process regression (GPR) model has been widely used to fit data when the regression function is unknown and its nice properties have been well established. In this article, we introduce an extended t-process regression (eTPR) model, a nonlinear model which allows a robust best linear unbiased predictor (BLUP). Owing to its succinct construction, it inherits many attractive properties from the GPR model, such as having closed forms of marginal and predictive distributions to give an explicit form for robust procedures, and easy to cope with large dimensional covariates with an efficient implementation. Properties of the robustness are studied. Simulation studies and real data applications show that the eTPR model gives a robust fit in the presence of outliers in both input and output spaces and has a good performance in prediction, compared with other existed methods.