{"title":"求解Lasso问题的数值算法综述","authors":"Yujie Zhao, X. Huo","doi":"10.1002/wics.1602","DOIUrl":null,"url":null,"abstract":"In statistics, the least absolute shrinkage and selection operator (Lasso) is a regression method that performs both variable selection and regularization. There is a lot of literature available, discussing the statistical properties of the regression coefficients estimated by the Lasso method. However, there lacks a comprehensive review discussing the algorithms to solve the optimization problem in Lasso. In this review, we summarize five representative algorithms to optimize the objective function in Lasso, including iterative shrinkage threshold algorithm (ISTA), fast iterative shrinkage‐thresholding algorithms (FISTA), coordinate gradient descent algorithm (CGDA), smooth L1 algorithm (SLA), and path following algorithm (PFA). Additionally, we also compare their convergence rate, as well as their potential strengths and weakness.","PeriodicalId":47779,"journal":{"name":"Wiley Interdisciplinary Reviews-Computational Statistics","volume":" ","pages":""},"PeriodicalIF":4.4000,"publicationDate":"2022-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":"{\"title\":\"A survey of numerical algorithms that can solve the Lasso problems\",\"authors\":\"Yujie Zhao, X. Huo\",\"doi\":\"10.1002/wics.1602\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In statistics, the least absolute shrinkage and selection operator (Lasso) is a regression method that performs both variable selection and regularization. There is a lot of literature available, discussing the statistical properties of the regression coefficients estimated by the Lasso method. However, there lacks a comprehensive review discussing the algorithms to solve the optimization problem in Lasso. In this review, we summarize five representative algorithms to optimize the objective function in Lasso, including iterative shrinkage threshold algorithm (ISTA), fast iterative shrinkage‐thresholding algorithms (FISTA), coordinate gradient descent algorithm (CGDA), smooth L1 algorithm (SLA), and path following algorithm (PFA). Additionally, we also compare their convergence rate, as well as their potential strengths and weakness.\",\"PeriodicalId\":47779,\"journal\":{\"name\":\"Wiley Interdisciplinary Reviews-Computational Statistics\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":4.4000,\"publicationDate\":\"2022-10-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Wiley Interdisciplinary Reviews-Computational Statistics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1002/wics.1602\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Wiley Interdisciplinary Reviews-Computational Statistics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1002/wics.1602","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
A survey of numerical algorithms that can solve the Lasso problems
In statistics, the least absolute shrinkage and selection operator (Lasso) is a regression method that performs both variable selection and regularization. There is a lot of literature available, discussing the statistical properties of the regression coefficients estimated by the Lasso method. However, there lacks a comprehensive review discussing the algorithms to solve the optimization problem in Lasso. In this review, we summarize five representative algorithms to optimize the objective function in Lasso, including iterative shrinkage threshold algorithm (ISTA), fast iterative shrinkage‐thresholding algorithms (FISTA), coordinate gradient descent algorithm (CGDA), smooth L1 algorithm (SLA), and path following algorithm (PFA). Additionally, we also compare their convergence rate, as well as their potential strengths and weakness.