Parameter Estimation for Gaussian Process c-Regression Models Based on Marginal Likelihood Maximization

Abstract

The c-regression model (CRM) is a method that simultaneously performs clustering and regression. CRM is based on linear regression, which has the disadvantage of not obtaining a nonlinear structure. To overcome this drawback, a c-regression model based on Gaussian process regression (GPCRM), which extends CRM to Gaussian process regression, has been proposed. Gaussian process regression is a method for estimating nonlinear regression lines using kernel functions, which are inner products of feature spaces. Although GPCRM can handle nonlinear structures, it has been reported that underfitting can occur depending on the kernel parameters, resulting in large residuals in the regression line. Therefore, this paper proposes Maximum Marginal Likelihood Gaussian Process based c-Regression Models as a method to maximize the marginal likelihood and optimize the kernel parameters. Numerical experiments suggest that the proposed method divides the data by finding a regression line with smaller residuals than the existing method.