HiQR：带惩罚的高维二次回归高效算法

IF 1.5 3区数学 Q3 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Computational Statistics & Data Analysis Pub Date : 2023-12-28 DOI:10.1016/j.csda.2023.107904

Cheng Wang , Haozhe Chen , Binyan Jiang

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引用次数: 0

摘要

本文研究了高维环境下惩罚性二次回归的高效解决方案。利用交互回归的矩阵结构，提出了一种新颖高效的脊惩罚二次回归算法。此外，还开发了一种交替方向乘法（ADMM）框架，用于具有一般惩罚的惩罚性二次回归，包括单一惩罚函数和混合惩罚函数。该方法将计算简化为基于矩阵的基本操作，因此在内存存储和计算复杂度方面都很有吸引力，可用于解决高维环境中的惩罚二次回归问题。

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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HiQR: An efficient algorithm for high-dimensional quadratic regression with penalties

This paper investigates the efficient solution of penalized quadratic regressions in high-dimensional settings. A novel and efficient algorithm for ridge-penalized quadratic regression is proposed, leveraging the matrix structures of the regression with interactions. Additionally, an alternating direction method of multipliers (ADMM) framework is developed for penalized quadratic regression with general penalties, including both single and hybrid penalty functions. The approach simplifies the calculations to basic matrix-based operations, making it appealing in terms of both memory storage and computational complexity for solving penalized quadratic regressions in high-dimensional settings.

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来源期刊

Computational Statistics & Data Analysis 数学-计算机：跨学科应用

CiteScore

3.70

自引率

5.60%

发文量

167

审稿时长

60 days

期刊介绍： Computational Statistics and Data Analysis (CSDA), an Official Publication of the network Computational and Methodological Statistics (CMStatistics) and of the International Association for Statistical Computing (IASC), is an international journal dedicated to the dissemination of methodological research and applications in the areas of computational statistics and data analysis. The journal consists of four refereed sections which are divided into the following subject areas: I) Computational Statistics - Manuscripts dealing with: 1) the explicit impact of computers on statistical methodology (e.g., Bayesian computing, bioinformatics,computer graphics, computer intensive inferential methods, data exploration, data mining, expert systems, heuristics, knowledge based systems, machine learning, neural networks, numerical and optimization methods, parallel computing, statistical databases, statistical systems), and 2) the development, evaluation and validation of statistical software and algorithms. Software and algorithms can be submitted with manuscripts and will be stored together with the online article. II) Statistical Methodology for Data Analysis - Manuscripts dealing with novel and original data analytical strategies and methodologies applied in biostatistics (design and analytic methods for clinical trials, epidemiological studies, statistical genetics, or genetic/environmental interactions), chemometrics, classification, data exploration, density estimation, design of experiments, environmetrics, education, image analysis, marketing, model free data exploration, pattern recognition, psychometrics, statistical physics, image processing, robust procedures. [...] III) Special Applications - [...] IV) Annals of Statistical Data Science [...]