Deterministic error bounds for kernel-based learning techniques under bounded noise

被引：19

作者：

Maddalena, Emilio Tanowe ^{[1
]}

Scharnhorst, Paul ^{[1
,2
]}

Jones, Colin N. ^{[1
]}

机构：

[1] Ecole Polytech Fed Lausanne EPFL, Automat Control Lab, Lausanne, Switzerland

[2] CSEM SA, Neuchatel, Switzerland

来源：

AUTOMATICA | 2021年 / 134卷

基金：

瑞士国家科学基金会;

关键词：

Deterministic error bounds; Generalization error; Kernel ridge regression; Support vector machines; SYSTEM-IDENTIFICATION; REGRESSION; RATES;

D O I：

10.1016/j.automatica.2021.109896

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

We consider the problem of reconstructing a function from a finite set of noise-corrupted samples. Two kernel algorithms are analyzed, namely kernel ridge regression and epsilon-support vector regression. By assuming the ground-truth function belongs to the reproducing kernel Hilbert space of the chosen kernel, and the measurement noise affecting the dataset is bounded, we adopt an approximation theory viewpoint to establish deterministic, finite-sample error bounds for the two models. Finally, we discuss their connection with Gaussian processes and two numerical examples are provided. In establishing our inequalities, we hope to help bring the fields of non-parametric kernel learning and system identification for robust control closer to each other. (C) 2021 Elsevier Ltd. All rights reserved.

引用

页数：9

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