Kernel-Based Regressors Equivalent to Stochastic Affine Estimators

Akira TANAKA; Masanari NAKAMURA; Hideyuki IMAI

doi:10.1587/transinf.2021EDP7156

Kernel-Based Regressors Equivalent to Stochastic Affine Estimators

Akira TANAKA, Masanari NAKAMURA, Hideyuki IMAI

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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.

Publication: IEICE TRANSACTIONS on Information Vol.E105-D No.1 pp.116-122

Publication Date: 2022/01/01

Publicized: 2021/10/05

Online ISSN: 1745-1361

DOI: 10.1587/transinf.2021EDP7156

Type of Manuscript: PAPER

Category: Artificial Intelligence, Data Mining

Authors

Akira TANAKA
  Hokkaido University
Masanari NAKAMURA
  Hokkaido University
Hideyuki IMAI
  Hokkaido University

Keyword

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

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Akira TANAKA, Masanari NAKAMURA, Hideyuki IMAI, "Kernel-Based Regressors Equivalent to Stochastic Affine Estimators" in IEICE TRANSACTIONS on Information, vol. E105-D, no. 1, pp. 116-122, January 2022, doi: 10.1587/transinf.2021EDP7156.
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.
URL: https://global.ieice.org/en_transactions/information/10.1587/transinf.2021EDP7156/_p

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@ARTICLE{e105-d_1_116,
author={Akira TANAKA, Masanari NAKAMURA, Hideyuki IMAI, },
journal={IEICE TRANSACTIONS on Information},
title={Kernel-Based Regressors Equivalent to Stochastic Affine Estimators},
year={2022},
volume={E105-D},
number={1},
pages={116-122},
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.},
keywords={},
doi={10.1587/transinf.2021EDP7156},
ISSN={1745-1361},
month={January},}

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TY - JOUR
TI - Kernel-Based Regressors Equivalent to Stochastic Affine Estimators
T2 - IEICE TRANSACTIONS on Information
SP - 116
EP - 122
AU - Akira TANAKA
AU - Masanari NAKAMURA
AU - Hideyuki IMAI
PY - 2022
DO - 10.1587/transinf.2021EDP7156
JO - IEICE TRANSACTIONS on Information
SN - 1745-1361
VL - E105-D
IS - 1
JA - IEICE TRANSACTIONS on Information
Y1 - January 2022
AB - 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.
ER -