Kernel Ridge Regression with Autocorrelation Prior: Optimal Model and Cross-Validation

Abstract

Kernel regression problem with autocorrelation prior is discussed in this paper. We revealed the optimal model of the kernel ridge regression in terms of the expected generalization error under the assumed autocorrelation prior. This result agrees with the optimal model of the Gaussian process regression, whose optimality is specified by the conditional expectation by a given set of training samples. We also proved that the minimizer of the expected cross-validation criterion is reduced to the optimal model, which gives a novel aspect of nonasymptotic theoretical justification of the cross-validation technique in the kernel regression problem.