{"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/adaptive-huber-regression","title":"Adaptive Huber Regression","arxiv_id":"1706.06991","date":"2017-06-21","proceeding":null,"authors":["Qiang Sun","Wenxin Zhou","Jianqing Fan"],"abstract":"Big data can easily be contaminated by outliers or contain variables with heavy-tailed distributions, which makes many conventional methods inadequate. To address this challenge, we propose the adaptive Huber regression for robust estimation and inference. The key observation is that the robustification parameter should adapt to the sample size, dimension and moments for optimal tradeoff between bias and robustness. Our theoretical framework deals with heavy-tailed distributions with bounded $(1+\\delta)$-th moment for any $\\delta > 0$. We establish a sharp phase transition for robust estimation of regression parameters in both low and high dimensions: when $\\delta \\geq 1$, the estimator admits a sub-Gaussian-type deviation bound without sub-Gaussian assumptions on the data, while only a slower rate is available in the regime $0<\\delta< 1$. Furthermore, this transition is smooth and optimal. In addition, we extend the methodology to allow both heavy-tailed predictors and observation noise. Simulation studies lend further support to the theory. In a genetic study of cancer cell lines that exhibit heavy-tailedness, the proposed methods are shown to be more robust and predictive.","url_abs":"https://arxiv.org/abs/1706.06991v2","url_pdf":"https://arxiv.org/pdf/1706.06991v2.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":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"adaptive-huber-regression","repo_url":"https://github.com/fd0r/adaptative_huber_regression","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"adaptive-huber-regression","repo_url":"https://github.com/rruimao/ACLS","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"unanswered"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1706.06991","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1706.06991"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. Samples come from repositories linked to the paper, official or community; repo_kind says which.","repos":[{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/rruimao/ACLS","reach":{"status":"unanswered"}},{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/fd0r/adaptative_huber_regression","reach":null}],"summary":{"ran_honours":1},"by_repo_kind":{"listed":{"samples":1,"ran":1,"repositories":1}},"repo_kind_vocabulary":{"official":"The archive marks this repository official for the paper","named_in_paper":"The archive records that the paper mentions this repository; it is not marked official","listed":"In the archive's code links for this paper, not marked official and not recorded as mentioned in the paper","found_in_text":"Syntology found this repository in the paper's own text; whether it is the authors' implementation is not asserted","community":"Not in the archive's code links for this paper; a community repository Syntology harvested"},"n_pointer_only_for_licence":1,"samples":[{"code_sha256_prefix":"a19ff5e12a616a64","entry":"soft_thresholding","repo":"fd0r/adaptative_huber_regression","repo_kind":"listed","path":"ada_hub/huber_regressor.py","file_url":"https://github.com/fd0r/adaptative_huber_regression/blob/HEAD/ada_hub/huber_regressor.py","link_basis":"first_harvest_node","language":"python","status":"ran_honours","verification_level":1,"contract_check":"HONOURS","metamorphic_tier":"invariant","behaviour_fingerprint":true,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"a19ff5e12a616a64"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}