{"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/on-the-convergence-of-irls-and-its-variants","title":"On the Convergence of IRLS and Its Variants in Outlier-Robust Estimation","arxiv_id":null,"date":"2023-01-01","proceeding":"CVPR 2023 1","authors":["Liangzu Peng","Christian Kümmerle","René Vidal"],"abstract":"    Outlier-robust estimation involves estimating some parameters (e.g., 3D rotations) from data samples in the presence of outliers, and is typically formulated as a non-convex and non-smooth problem. For this problem, the classical method called iteratively reweighted least-squares (IRLS) and its variants have shown impressive performance. This paper makes several contributions towards understanding why these algorithms work so well. First, we incorporate majorization and graduated non-convexity (GNC) into the IRLS framework and prove that the resulting IRLS variant is a convergent method for outlier-robust estimation. Moreover, in the robust regression context with a constant fraction of outliers, we prove this IRLS variant converges to the ground truth at a global linear and local quadratic rate for a random Gaussian feature matrix with high probability. Experiments corroborate our theory and show that the proposed IRLS variant converges within 5-10 iterations for typical problem instances of outlier-robust estimation, while state-of-the-art methods need at least 30 iterations. A basic implementation of our method is provided: https://github.com/liangzu/IRLS-CVPR2023    ","url_abs":"http://openaccess.thecvf.com//content/CVPR2023/html/Peng_On_the_Convergence_of_IRLS_and_Its_Variants_in_Outlier-Robust_CVPR_2023_paper.html","url_pdf":"http://openaccess.thecvf.com//content/CVPR2023/papers/Peng_On_the_Convergence_of_IRLS_and_Its_Variants_in_Outlier-Robust_CVPR_2023_paper.pdf","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":"on-the-convergence-of-irls-and-its-variants","repo_url":"https://github.com/liangzu/irls-cvpr2023","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}