统计回归模型及其优化算法综述  

A survey on statistical regression models and optimization algorithms

作　　者：方升 梁飞豹[1] 刘勇进 FANG Sheng;LIANG Feibao;LIU Yongjin(College of Mathematics and Statistics,Fuzhou University,Fuzhou,Fujian 350108,China)

机构地区：[1]福州大学数学与统计学院,福建福州350108

出　　处：《福州大学学报（自然科学版）》2021年第5期638-654,共17页Journal of Fuzhou University(Natural Science Edition)

基　　金：国家自然科学基金面上资助项目(11871153);福建省自然科学基金面上资助项目(2019J01644)。

摘　　要：在大数据时代,正则化(惩罚)回归模型成为高维数据分析的一种有效分析工具.文中从统计模型理论和优化算法两个角度对正则化回归模型进行简要的概述,主要介绍线性回归模型、广义线性模型和分位数回归模型三种经典且重要的回归模型以及相应的正则项.对于线性回归模型,介绍最小二乘回归和l 1-正则最小二乘回归问题的优化算法;对广义线性模型和分位数回归模型,介绍逻辑回归模型和求解l 1-正则逻辑回归问题的优化算法,并展示分位数回归模型和求解相应的正则化分位数回归模型的优化算法.最后,对正则化回归模型未来的研究方向进行展望.In big data era,regularized(penalized)regression model becomes an effective tool in high-dimensional data analysis.This survey reviews the regularized regression models and the optimization algorithms for solving them during the last few decades.The paper mainly introduces regularized terms and three classical and important regression models:linear regression model,generalized linear model and quantile regression model.For the linear regression model,we give a brief introduction of the least squares regression and summarize the optimization algorithms for solving the l 1-regularized least squares regression.For the generalized linear model,we focus on the logistic regression model and algorithms for the l 1-regularized logistic regression problem.Also,we introduce the quantile regression model and the optimization methods for the regularized quantile regression problem.Finally,we conclude the paper and propose the possible future research direction.

关 键 词：统计回归模型 优化算法 线性回归模型 广义线性模型 分位数回归模型 

分 类 号：O224[理学—运筹学与控制论]