Kernel-Based Regressors Equivalent to Stochastic Affine Estimators

• TANAKA Akira

  Division of Computer Science and Information Technology, Faculty of Information Science and Technology, Hokkaido University

• NAKAMURA Masanari

  Division of Computer Science and Information Technology, Faculty of Information Science and Technology, Hokkaido University

• IMAI Hideyuki

  Division of Computer Science and Information Technology, Faculty of Information Science and Technology, Hokkaido University

Abstract

The solution of the ordinary kernel ridge regression, based on the squared loss function and the squared norm-based regularizer, can be easily interpreted as a stochastic linear estimator by considering the autocorrelation prior for an unknown true function. As is well known, a stochastic affine estimator is one of the simplest extensions of the stochastic linear estimator. However, its corresponding kernel regression problem is not revealed so far. In this paper, we give a formulation of the kernel regression problem, whose solution is reduced to a stochastic affine estimator, and also give interpretations of the formulation.

Journal

• IEICE Transactions on Information and Systems

  IEICE Transactions on Information and Systems E105.D (1), 116-122, 2022-01-01

  The Institute of Electronics, Information and Communication Engineers

Keywords

• kernel regression
• autocorrelation prior
• linear estimators
• affine estimators
• optimization criterion

Details

• CRID: 1390572092344736768
• NII Article ID: 130008138820
• DOI: 10.1587/transinf.2021edp7156
• ISSN: 17451361
• ISSN: 09168532
• Web Site: https://www.jstage.jst.go.jp/article/transinf/E105.D/1/E105.D_2021EDP7156/_pdf
• Text Lang: en
• Data Source:
  • JaLC
  • Crossref
  • CiNii Articles
  • KAKEN
• Abstract License Flag: Disallowed