{"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/revisiting-differentially-private-linear","title":"Revisiting differentially private linear regression: optimal and adaptive prediction & estimation in unbounded domain","arxiv_id":"1803.02596","date":"2018-03-07","proceeding":null,"authors":["Yu-Xiang Wang"],"abstract":"We revisit the problem of linear regression under a differential privacy\nconstraint. By consolidating existing pieces in the literature, we clarify the\ncorrect dependence of the feature, label and coefficient domains in the\noptimization error and estimation error, hence revealing the delicate price of\ndifferential privacy in statistical estimation and statistical learning.\nMoreover, we propose simple modifications of two existing DP algorithms: (a)\nposterior sampling, (b) sufficient statistics perturbation, and show that they\ncan be upgraded into **adaptive** algorithms that are able to exploit\ndata-dependent quantities and behave nearly optimally **for every instance**.\nExtensive experiments are conducted on both simulated data and real data, which\nconclude that both AdaOPS and AdaSSP outperform the existing techniques on\nnearly all 36 data sets that we test on.","url_abs":"http://arxiv.org/abs/1803.02596v2","url_pdf":"http://arxiv.org/pdf/1803.02596v2.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":"revisiting-differentially-private-linear","repo_url":"https://github.com/yuxiangw/optimal_dp_linear_regression","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}},{"paper_slug":"revisiting-differentially-private-linear","repo_url":"https://github.com/TPiazza21/Thesis","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}}],"tasks":[{"task_slug":"regression-1","task_name":"regression"}],"methods":[{"method_slug":"linear-regression","method_name":"Linear Regression"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1803.02596","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}