Variable Selection for Nonparametric Learning with Power Series Kernels

TL;DR

This paper introduces a variable selection method for nonparametric kernel-based estimation that achieves consistency and is applicable to various kernel methods, supported by theoretical proofs and empirical results.

Contribution

It extends variable selection consistency to kernel estimators using power series kernels, combining two-stage estimation with l1-penalization.

Findings

Method achieves variable selection consistency with power series kernels.

Effective in kernel ridge regression, density, and density-ratio estimation.

Validated through simulations and real data applications.

Abstract

In this paper, we propose a variable selection method for general nonparametric kernel-based estimation. The proposed method consists of two-stage estimation: (1) construct a consistent estimator of the target function, (2) approximate the estimator using a few variables by l1-type penalized estimation. We see that the proposed method can be applied to various kernel nonparametric estimation such as kernel ridge regression, kernel-based density and density-ratio estimation. We prove that the proposed method has the property of the variable selection consistency when the power series kernel is used. This result is regarded as an extension of the variable selection consistency for the non-negative garrote to the kernel-based estimators. Several experiments including simulation studies and real data applications show the effectiveness of the proposed method.