On a class of linear regression methods

IF 1.8 2区数学 Q1 MATHEMATICS

Journal of Complexity Pub Date : 2024-01-09 DOI:10.1016/j.jco.2024.101826

Ying-Ao Wang , Qin Huang , Zhigang Yao , Ye Zhang

引用次数: 0

Abstract

In this paper, a unified study is presented for the design and analysis of a broad class of linear regression methods. The proposed general framework includes the conventional linear regression methods (such as the least squares regression and the Ridge regression) and some new regression methods (e.g. the Landweber regression and Showalter regression), which have recently been introduced in the fields of optimization and inverse problems. The strong consistency, the reduced mean squared error, the asymptotic Gaussian property, and the best worst case error of this class of linear regression methods are investigated. Various numerical experiments are performed to demonstrate the consistency and efficiency of the proposed class of methods for linear regression.

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关于一类线性回归方法

本文提出了对一大类线性回归方法的设计和分析的统一研究。所提出的总体框架包括传统的线性回归方法（如最小二乘回归和岭回归）和一些新的回归方法（如 Landweber 回归和 Showalter 回归），这些方法是最近在优化和逆问题领域提出的。研究了这一类线性回归方法的强一致性、减小的均方误差、渐近高斯特性和最佳最坏情况误差。通过各种数值实验证明了所提出的线性回归方法的一致性和效率。

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.