核岭回归的自适应参数选择

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Applied and Computational Harmonic Analysis Pub Date : 2024-06-07 DOI:10.1016/j.acha.2024.101671

Shao-Bo Lin

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引用次数: 0

摘要

本文重点讨论核岭回归（KRR）的参数选择问题。由于 KRR 特殊的频谱特性，我们发现参数区间的精细细分会缩小两个连续 KRR 估计值之间的差异。基于这一观察结果，我们根据所谓的 Lepski 型原理，为 KRR 开发了一种早期停止型参数选择策略。我们在学习理论的框架下进行了理论验证，结果表明，采用所提出的参数选择策略的 KRR 能够成功地获得最佳学习率，并能适应不同的规范，为核方法的参数选择提供了新的记录。

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Adaptive parameter selection for kernel ridge regression

This paper focuses on parameter selection issues of kernel ridge regression (KRR). Due to special spectral properties of KRR, we find that delicate subdivision of the parameter interval shrinks the difference between two successive KRR estimates. Based on this observation, we develop an early-stopping type parameter selection strategy for KRR according to the so-called Lepskii-type principle. Theoretical verifications are presented in the framework of learning theory to show that KRR equipped with the proposed parameter selection strategy succeeds in achieving optimal learning rates and adapts to different norms, providing a new record of parameter selection for kernel methods.

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来源期刊

Applied and Computational Harmonic Analysis 物理-物理：数学物理

CiteScore

5.40

自引率

4.00%

发文量

审稿时长

22.9 weeks

期刊介绍： Applied and Computational Harmonic Analysis (ACHA) is an interdisciplinary journal that publishes high-quality papers in all areas of mathematical sciences related to the applied and computational aspects of harmonic analysis, with special emphasis on innovative theoretical development, methods, and algorithms, for information processing, manipulation, understanding, and so forth. The objectives of the journal are to chronicle the important publications in the rapidly growing field of data representation and analysis, to stimulate research in relevant interdisciplinary areas, and to provide a common link among mathematical, physical, and life scientists, as well as engineers.