{"id":946512,"date":"2023-06-07T09:48:46","date_gmt":"2023-06-07T16:48:46","guid":{"rendered":"https:\/\/find.codeghost.online\/en-us\/research\/?post_type=msr-research-item&#038;p=946512"},"modified":"2023-06-08T11:28:30","modified_gmt":"2023-06-08T18:28:30","slug":"statistical-learning-under-heterogenous-distribution-shift","status":"publish","type":"msr-research-item","link":"https:\/\/find.codeghost.online\/en-us\/research\/publication\/statistical-learning-under-heterogenous-distribution-shift\/","title":{"rendered":"Statistical Learning under Heterogenous Distribution Shift"},"content":{"rendered":"\n\n\n<p class=\"wp-block-paragraph\">This paper studies the prediction of a target\u00a0\\(z\\)\u00a0from a pair of random variables\u00a0\\((x,y)\\), where the ground-truth predictor is additive\u00a0\\(E[z\u2223x,y]=f_\u22c6(x)+g_\u22c6(y)\\). We study the performance of empirical risk minimization (ERM) over functions\u00a0\\(f+g\\),\u00a0\\(f\\in F\\)\u00a0and\u00a0\\(g\\in G\\), fit on a given training distribution, but evaluated on a test distribution which exhibits covariate shift. We show that, when the class\u00a0<em>\\(F\\)<\/em>\u00a0is &#8220;simpler&#8221; than\u00a0<em>\\(G\\)<\/em>\u00a0(measured, e.g., in terms of its metric entropy), our predictor is more resilient to <em>heterogenous covariate shifts<\/em> in which the shift in\u00a0<strong>\\(x\\)<\/strong>\u00a0is much greater than that in\u00a0<strong>\\(y\\)<\/strong>. These results rely on a novel H\u00f6lder style inequality for the Dudley integral which may be of independent interest. Moreover, we corroborate our theoretical findings with experiments demonstrating improved resilience to shifts in &#8220;simpler&#8221; features across numerous domains.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>This paper studies the prediction of a target\u00a0\u00a0from a pair of random variables\u00a0, where the ground-truth predictor is additive\u00a0. We study the performance of empirical risk minimization (ERM) over functions\u00a0,\u00a0\u00a0and\u00a0, fit on a given training distribution, but evaluated on a test distribution which exhibits covariate shift. We show that, when the class\u00a0\u00a0is &#8220;simpler&#8221; than\u00a0\u00a0(measured, e.g., [&hellip;]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr-author-ordering":[{"type":"text","value":"Max Simchowitz","user_id":0},{"type":"text","value":"Anurag Ajay","user_id":0},{"type":"text","value":"Pulkit Agrawal","user_id":0},{"type":"user_nicename","value":"Akshay Krishnamurthy","user_id":"30913"}],"msr_publishername":"","msr_publisher_other":"","msr_booktitle":"","msr_chapter":"","msr_edition":"","msr_editors":"","msr_how_published":"","msr_isbn":"","msr_issue":"","msr_journal":"","msr_number":"","msr_organization":"","msr_pages_string":"","msr_page_range_start":"","msr_page_range_end":"","msr_series":"","msr_volume":"","msr_copyright":"","msr_conference_name":"ICML 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