A Robust t-process Regression Model with Independent Errors

TL;DR

This paper introduces a new robust t-process regression model that allows for independent errors, improving outlier robustness and prediction accuracy over existing dependent-error models.

Contribution

It proposes a novel robust process regression framework with independent errors, along with an efficient estimation method and theoretical properties.

Findings

Model is robust against outliers

Outperforms existing models in prediction accuracy

Estimated random-effects help detect outliers

Abstract

Gaussian process regression (GPR) model is well-known to be susceptible to outliers. Robust process regression models based on t-process or other heavy-tailed processes have been developed to address the problem. However, due to the nature of the current definition for heavy-tailed processes, the unknown process regression function and the random errors are always defined jointly and thus dependently. This definition, mainly owing to the dependence assumption involved, is not justified in many practical problems and thus limits the application of those robust approaches. It also results in a limitation of the theory of robust analysis. In this paper, we propose a new robust process regression model enabling independent random errors. An efficient estimation procedure is developed. Statistical properties, such as unbiasness and information consistency, are provided. Numerical studies show that the proposed method is robust against outliers and has a better performance in prediction compared with the existing models. We illustrate that the estimated random-effects are useful in detecting outlying curves.