Variable Selection for Nonparametric Learning with Power Series Kernels
Variable Selection for Nonparametric Learning with Power Series Kernels
复制标题
使用幂级数核进行非参数学习的变量选择
DOI：
10.1162/neco_a_01212
复制
发表时间：
2019
影响因子：
2.9
通讯作者：
Kanamori Takafumi
中科院分区：
文献类型：
--
作者：
Matsui Kota;Kumagai Wataru;Kanamori Kenta;Nishikimi Mitsuaki;Kanamori Takafumi
在这封信中，我们提出了一个一般的非参数核基估计的变量选择方法。所提出的方法包括两个阶段的估计：（1）构造一个目标函数的一致估计，和（2）近似估计使用几个变量的类型惩罚估计。我们看到，所提出的方法可以应用于各种核非参数估计，如核岭回归，基于核的密度，密度比估计。我们证明了当使用幂级数核时，所提出的方法具有变量选择一致性的性质。这里，幂级数核是一类包含多项式核和指数核的核。这个结果被认为是一个扩展的非负绞喉（NNG），自适应Lasso的特殊情况下，基于核的估计变量选择的一致性。仿真研究和真实的数据应用表明了该方法的有效性。
In this letter, 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, and (2) approximate the estimator using a few variables by-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 variable selection consistency when the power series kernel is used. Here, the power series kernel is a certain class of kernels containing polynomial and exponential kernels. This result is regarded as an extension of the variable selection consistency for the nonnegative garrote (NNG), 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.