Identifiability of Covariance Kernels in the Gaussian Process Regression Model

TL;DR

This paper investigates the identifiability of covariance kernel parameters in Gaussian process regression models, proving conditions for identifiability and illustrating cases where parameters are not identifiable.

Contribution

It establishes the theoretical identifiability of covariance kernel parameters in specific GPR models with mixed kernels, filling a gap in existing literature.

Findings

Proves identifiability of parameters in radial basis mixed kernel GPR.

Provides examples of non-identifiable cases in mixed kernel GPRs.

Enhances understanding of parameter inference in Gaussian process models.

Abstract

Gaussian process regression (GPR) model is a popular nonparametric regression model. In GPR, features of the regression function such as varying degrees of smoothness and periodicities are modeled through combining various covarinace kernels, which are supposed to model certain effects. The covariance kernels have unknown parameters which are estimated by the EM-algorithm or Markov Chain Monte Carlo. The estimated parameters are keys to the inference of the features of the regression functions, but identifiability of these parameters has not been investigated. In this paper, we prove identifiability of covariance kernel parameters in two radial basis mixed kernel GPR and radial basis and periodic mixed kernel GPR. We also provide some examples about non-identifiable cases in such mixed kernel GPRs.