Nonasymptotic analysis of robust regression with modified Huber's loss

IF 1.8 2区数学 Q1 MATHEMATICS

Journal of Complexity Pub Date : 2023-06-01 DOI:10.1016/j.jco.2023.101744

Hongzhi Tong

引用次数: 0

Abstract

To achieve robustness against the outliers or heavy-tailed sampling distribution, we consider an Ivanov regularized empirical risk minimization scheme associated with a modified Huber's loss for nonparametric regression in reproducing kernel Hilbert space. By tuning the scaling and regularization parameters in accordance with the sample size, we develop nonasymptotic concentration results for such an adaptive estimator. Specifically, we establish the best convergence rates for prediction error when the conditional distribution satisfies a weak moment condition.

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修正Huber损失鲁棒回归的非渐近分析

为了实现对离群值或重尾抽样分布的鲁棒性，我们考虑了一种带有修正Huber损失的Ivanov正则化经验风险最小化方案，用于再现核希尔伯特空间的非参数回归。通过根据样本大小调整尺度和正则化参数，我们得到了这种自适应估计器的非渐近集中结果。具体地说，我们建立了条件分布满足弱矩条件时预测误差的最佳收敛速率。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Complexity 工程技术-计算机：理论方法

CiteScore

3.10

自引率

17.60%

发文量

审稿时长

>12 weeks

期刊介绍： The multidisciplinary Journal of Complexity publishes original research papers that contain substantial mathematical results on complexity as broadly conceived. Outstanding review papers will also be published. In the area of computational complexity, the focus is on complexity over the reals, with the emphasis on lower bounds and optimal algorithms. The Journal of Complexity also publishes articles that provide major new algorithms or make important progress on upper bounds. Other models of computation, such as the Turing machine model, are also of interest. Computational complexity results in a wide variety of areas are solicited. Areas Include: • Approximation theory • Biomedical computing • Compressed computing and sensing • Computational finance • Computational number theory • Computational stochastics • Control theory • Cryptography • Design of experiments • Differential equations • Discrete problems • Distributed and parallel computation • High and infinite-dimensional problems • Information-based complexity • Inverse and ill-posed problems • Machine learning • Markov chain Monte Carlo • Monte Carlo and quasi-Monte Carlo • Multivariate integration and approximation • Noisy data • Nonlinear and algebraic equations • Numerical analysis • Operator equations • Optimization • Quantum computing • Scientific computation • Tractability of multivariate problems • Vision and image understanding.