Takafumi Kanamori

Variable Selection for Nonparametric Learning with Power Series Kernels

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 estimations 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. Here the power series kernel is a certain class of kernels containing the polynomial kernel and exponential kernel. This result is regarded as an extension of the variable selection consistency for the non-negative garrote, which is a special case of the adaptive lasso, to the kernel-based estimators. Several experiments including simulation studies and real data applications show the effectiveness of the proposed method. This is joint work with K. Matsui, W. Kumagai, K. Kanamori, and M. Nishikimi.