{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/imbalanced-mixed-linear-regression","title":"Imbalanced Mixed Linear Regression","arxiv_id":null,"date":"2023-09-21","proceeding":"NeurIPS 2023 11","authors":[],"abstract":"We consider the problem of mixed linear regression (MLR), where each observed sample belongs to one of $K$ unknown linear models. \nIn practical applications, the mixture of the $K$ models may be imbalanced with a significantly different number of samples from each model. Unfortunately, most MLR methods do not perform well in such settings. Motivated by this practical challenge, in this work we propose Mix-IRLS, a novel, simple and fast algorithm for MLR with excellent performance on both balanced and imbalanced mixtures.\nIn contrast to popular approaches that recover the $K$ models simultaneously, Mix-IRLS does it sequentially using tools from robust regression. Empirically, beyond imbalanced mixtures, Mix-IRLS succeeds in a broad range of additional settings where other methods fail, including small sample sizes, presence of outliers, and an unknown number of models $K$. Furthermore, Mix-IRLS outperforms competing methods on several real-world datasets, in some cases by a large margin. We complement our empirical results by deriving a recovery guarantee for Mix-IRLS, which highlights its advantage on imbalanced mixtures.","url_abs":"https://openreview.net/forum?id=MDxZYFR5Me","url_pdf":"https://openreview.net/pdf?id=MDxZYFR5Me","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"imbalanced-mixed-linear-regression","repo_url":"https://github.com/pizilber/mlr","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[{"method_slug":"linear-regression","method_name":"Linear Regression"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}