Variable Selection for Nonparametric Learning with Power Series Kernels
This work addresses variable selection in nonparametric learning for researchers and practitioners, offering an incremental extension of existing methods to kernel-based estimators.
The paper tackles variable selection for nonparametric kernel-based estimation by proposing a two-stage method that constructs a consistent estimator and approximates it with l1-type penalization, proving variable selection consistency with power series kernels and demonstrating effectiveness in experiments.
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.