[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-85453-en":3,"doc-seo-85453-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},85453,549758146520,"Patrick","https://ap-avatar.wpscdn.com/avatar/80002397d8c0411e94?_k=1775819394049821470",8,"Research & Report","Efficient Group Lasso Regularized Rank Regression with Simulation-Based Tuning","High-dimensional regression often breaks down under heavy-tailed noise and outliers, undermining least-squares reliability. The study develops a robust, non-smooth Wilcoxon-score rank objective combined with group sparsity regularization. Building on tuning-free results for rank Lasso, a simulation-based tuning rule is proposed and a finite-sample error bound is established. A proximal augmented Lagrangian algorithm is designed, with convergence analysis via metric subregularity of a non-polyhedral KKT mapping and semismooth Newton updates.","arXiv :2510 . 11546v3 [ stat .ML] 11 Jul 2026  \nEfficient Group Lasso Regularized Rank Regression with  \nSimulation-Based Tuning  \nMeixia Lin  \nSchool of Statistics and Data Science, Renmin University of China, P.R. China  \n[lin_meixia@ruc. edu. cn](lin_meixia@ruc. edu. cn)  \nMengjiao Shi  \nSchool of Mathematics and Statistics, Henan University, P.R. China  \n[smj@henu. edu. cn](smj@henu. edu. cn)  \nYunhai Xiao*  \nSchool of Mathematics and Statistics & Center for Applied Mathematics of Henan Province,  \nHenan University, P.R. China  \n[yhxiao@henu. edu. cn](yhxiao@henu. edu. cn) ∗  \nQian Zhang  \nEngineering Systems and Design, Singapore University of Technology and Design, Singapore  \n[qian_zhang@sutd. edu. sg](qian_zhang@sutd. edu. sg)  \nAbstract  \nHigh-dimensional regression often suffers from heavy-tailed noise and outliers, which can severely undermine the reliability of least-squares based methods. To improve robustness, we adopt a non-smooth Wilcoxon score based rank objective and incorporate the group sparsity regularization. By extending the tuning-free property originally developed for the rank Lasso, we introduce a simulation-based tuning rule and further establish a finite-sample error bound for the resulting estimator. To solve the associated optimization problem, we develop a proximal augmented Lagrangian method, for which we provide a novel convergence analysis by proving the metric subregularity of the underlying non-polyhedral KKT mapping, while enabling efficient semismooth Newton updates for the subproblems. Extensive numerical experiments demonstrate the robustness and effectiveness of our proposed estimator against several leading alternatives, and showcase the efficiency and scalability of our algorithm compared to the state-of-the-art baseline in both simulated and real-data settings.  \nKeywords: Rank-based regression Group Lasso regularization Simulation-based tuning Proximal augmented Lagrangian method  \n1 Introduction  \nConsider the standard linear model  \ny = Xβ∗ + ϵ, (1)  \n∗ * Corresponding author.  \nwhere y ∈ Rn is the response vector, X ∈ Rn×p is the design matrix with rows Xi representing the covariate vector for the i-th observation, β∗ ∈ Rp is the true coefficient vector, and ϵ ∈ Rn denotes the random error vector. Ordinary least squares is the classical approach for estimating β ∗ and works well under light-tailed noise like Gaussian errors. However, its reliance on the squared loss makes it highly sensitive to heavy-tailed errors and outliers. In particular, a single extreme value can dominate the loss function, leading to highly unstable estimates and compromised predictive performance. Yet, heavy-tailed errors are common in modern high-dimensional data, for example in genomics (Wang et al. , 2015) and neuroimaging (Eklund et al. , 2016), underscoring the need for robust regression methods that remain reliable in such settings.  \nTo address this issue, a variety of robust estimation techniques have been developed. One line of research employs robust loss functions, which mainly rely on truncation or downweighting strategies. For example, the Huber estimator (Huber, 1973 ; Sun et al. , 2020) is a classic truncation-based method, which clips gradients beyond a threshold to enforce linear growth, thereby diminishing the influence of outliers. In addition, Tukey’s biweight estimation (Beaton and Tukey, 1974 ; Huber, 2011) exemplifies the downweighting approach by adopting a bisquare function that reduces the weights of large residuals to zero. While these methods effectively alleviate the impact of outliers via gradient modification, they suffer from an identifiability issue as the global minimizers of the modified losses may not coincide with the true parameter vector (Fan et al. , 2016) . An alternative direction is quantile regression (Koenker and Bassett, 1978 ; Koenker, 2005), which replaces the squared loss with an asymmetric linear loss to estimate conditional quantiles, thereby providing ro","cbCaipLUfscgeh72","https://ap.wps.com/l/cbCaipLUfscgeh72","pdf",988918,3,1,44,"English","en",105,"# Introduction\n## Linear model and robustness motivation\n## Robust alternatives and rank-based methods\n## Rank loss and high-dimensional regularization","[{\"question\":\"Why do least-squares methods become unreliable in high-dimensional regression with heavy-tailed errors?\",\"answer\":\"Least-squares relies on squared loss, so single extreme observations can dominate the objective, producing unstable coefficient estimates and degraded predictive performance.\"},{\"question\":\"How does the proposed method improve robustness?\",\"answer\":\"It replaces the squared loss with a non-smooth Wilcoxon score–based rank objective and adds group sparsity regularization to handle outliers while enabling structured variable selection.\"},{\"question\":\"What is the role of simulation-based tuning in this framework?\",\"answer\":\"The approach extends tuning-free ideas from rank Lasso by introducing a simulation-based rule for selecting tuning parameters, accompanied by a finite-sample error bound for the resulting estimator.\"}]",1784203664,111,{"code":4,"msg":31,"data":32},"ok",{"site_id":25,"language":24,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"efficient-group-lasso-regularized-rank-regression-with-simulation-based-tuning","",{"@graph":36,"@context":85},[37,53,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,50],{"item":41,"name":42,"@type":43,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":20},"https://docshare.wps.com/document/research-report/",{"item":51,"name":13,"@type":43,"position":52},"https://docshare.wps.com/document/efficient-group-lasso-regularized-rank-regression-with-simulation-based-tuning/85453/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":24,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":41,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-25","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"Why do least-squares methods become unreliable in high-dimensional regression with heavy-tailed errors?","Question",{"text":75,"@type":76},"Least-squares relies on squared loss, so single extreme observations can dominate the objective, producing unstable coefficient estimates and degraded predictive performance.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does the proposed method improve robustness?",{"text":80,"@type":76},"It replaces the squared loss with a non-smooth Wilcoxon score–based rank objective and adds group sparsity regularization to handle outliers while enabling structured variable selection.",{"name":82,"@type":73,"acceptedAnswer":83},"What is the role of simulation-based tuning in this framework?",{"text":84,"@type":76},"The approach extends tuning-free ideas from rank Lasso by introducing a simulation-based rule for selecting tuning parameters, accompanied by a finite-sample error bound for the resulting estimator.","https://schema.org",{"og:url":51,"og:type":87,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":89,"canonical":51},"index,follow",{"doc_id":7,"site_id":25},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,123,128,131,135],{"id":21,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":52,"doc_module":4,"doc_module_name":46,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":46,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":46,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":132,"doc_module":4,"doc_module_name":46,"category_name":133,"show_sort_weight":132,"slug":134},10,"Lifestyle","lifestyle",{"id":136,"doc_module":4,"doc_module_name":46,"category_name":137,"show_sort_weight":106,"slug":138},19,"General","general"]