Variable Selection for Nonparametric Learning with Power Series Kernels

Matsui Kota; Kumagai Wataru; Kanamori Kenta; Nishikimi Mitsuaki; Kanamori Takafumi

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Variable Selection for Nonparametric Learning with Power Series Kernels

机译：使用幂级数核进行非参数学习的变量选择

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摘要

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 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 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.

机译：在这封信中，我们提出了一种基于常规非参数核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）构造目标函数的一致估计量；（2）通过l1型惩罚估计使用一些变量来近似估计量。我们看到，所提出的方法可以应用于各种核非参数估计，例如核脊回归，基于核的密度和密度比估计。我们证明了该方法在使用幂级数核时具有变量选择一致性的性质。在这里，幂级数内核是包含多项式和指数内核的一类内核。该结果被认为是非负Garrote（NNG）（自适应套索的特殊情况）的变量选择一致性向基于核的估计器的扩展。包括仿真研究和实际数据应用在内的一些实验证明了该方法的有效性。

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来源
《Neural computation》 |2019年第8期|1718-1750|共33页
作者
Matsui Kota; Kumagai Wataru; Kanamori Kenta; Nishikimi Mitsuaki; Kanamori Takafumi;
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作者单位

RIKEN Ctr Adv Intelligence Project Chuo Ku Tokyo 1030027 Japan;

Nagoya Inst Technol Dept Comp Sci Showa Ku Gokiso Cho Nagoya Aichi 4668555 Japan;

Nagoya Univ Grad Sch Med Dept Emergency & Crit Care Showa Ku Nagoya Aichi 4668550 Japan;

RIKEN Ctr Adv Intelligence Project Chuo Ku Tokyo 1030027 Japan|Tokyo Inst Technol Dept Math & Comp Sci Meguro Ku Tokyo 1528550 Japan;

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收录信息美国《科学引文索引》(SCI);美国《化学文摘》(CA);
原文格式 PDF
正文语种 eng
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2. Determination of coal properties using laser-induced breakdown spectroscopy combined with kernel extreme learning machine and variable selection [J] . Yan Chunhua, Qi Juan, Liang Jing, Journal of Analytical Atomic Spectrometry . 2018,第12期

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3. Discussion on “Doubly sparsity kernel learning with automatic variable selection and data extraction” [J] . Zhang Hao Helen Statistics and Its Interface . 2018,第3期

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4. Strong consistency of kernel-based local variable selection for nonlinear nonparametric systems [C] . Wenxiao Zhao, Han-Fu Chen, Er-Wei Bai, Australian Control Conference . 2016

机译：非线性非参数系统基于核的局部变量选择的强一致性
5. Kernel Methods in Nonparametric Functional Time Series [D] . Zhu, Tingyi. 2017

机译：非参数函数时间序列中的内核方法
6. Double Sparsity Kernel Learning with Automatic Variable Selection and Data Extraction [O] . Jingxiang Chen, Chong Zhang, Michael R. Kosorok, -1

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7. Kernel Dependent Functions in Nonparametric Regression with Fractional Time Series Errors kernel dependent function, bandwidth selection. [O] . Yuanhua Feng 100

机译：具有分数时间序列的非参数回归中的核依赖函数错误内核相关函数，带宽选择。

Variable Selection for Nonparametric Learning with Power Series Kernels

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