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The worst-case measure is formulated as a Gibbs probability measure, uniquely defined by maximizing expected loss under a relative-entropy constraint to a reference distribution. Derive closed-form expressions for key generalization metrics including expected-loss sensitivity, empirical-risk sensitivity, and the generalization gap, and recover known Gibbs-algorithm results such as expressing the gap via mutual information and lautum information. Establish a novel connection between the worst-case data-generating measure and the Gibbs algorithm by identifying shared structure across the model and data spaces.",{"@graph":69,"@context":123},[70,84,106],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/generalization-analysis-of-machine-learning-algorithms-via-the-worst-case-data-generating-probability-measure-290967/290967/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/generalization-analysis-of-machine-learning-algorithms-via-the-worst-case-data-generating-probability-measure-290967/290967.png","ImageObject",300,407,{"name":92,"@type":93},"Seraphina","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-01","2026-09-17",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",14,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What tool does the paper introduce to study generalization of machine learning algorithms?","Question",{"text":113,"@type":114},"It introduces the worst-case probability measure over the data to characterize machine learning generalization capabilities.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"How is the worst-case probability measure defined?",{"text":118,"@type":114},"It is identified as a Gibbs probability measure and is the unique solution to maximizing the expected loss under a relative-entropy constraint relative to a reference probability measure.",{"name":120,"@type":111,"acceptedAnswer":121},"Which generalization metrics are given closed-form expressions?",{"text":122,"@type":114},"The paper provides closed-form expressions for the sensitivity of the expected loss, the sensitivity of the empirical risk, and the generalization gap, all involving the worst-case data-generating probability measure.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},290967,1789643065,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":52,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":130,"read_time":144,"preview_page_count":4},962075114101,"https://ap-avatar.wpscdn.com/avatar/e000253a75eb197efd?x-image-process=image/resize,m_fixed,w_180,h_180&k=1780044092746381165","This is a repository copy of Generalization analysis of machine learning algorithms via the worst-case data-generating probability measure.  \nWhite Rose Research Online URL for this paper:  \n[https://eprints.whiterose.ac.uk/209027/](https://eprints.whiterose.ac.uk/209027/)  \n[Version: Accepted Version](Version: Accepted Version)  \nProceedings Paper:  \nZou, X., Perlaza, S.M., Esnaola, [J. orcid.org/0000-0001-5597-1718](J. orcid.org/0000-0001-5597-1718) et al. (1 more author)(2024) Generalization analysis of machine learning algorithms via the worst-case datagenerating probability measure. In: Proceedings of the 38th AAAI Conference on Artificial Intelligence. 38th Annual AAAI Conference on Artificial Intelligence, 20-27 Feb 2024, Vancouver, Canada. Association for the Advancement of Artificial Intelligence , pp. 17271- 17279. ISBN 9781577358879  \n[https://doi.org/10.1609/aaai.v38i15.29674](https://doi.org/10.1609/aaai.v38i15.29674)  \n© 2024 The Authors. Except as otherwise noted, this author-accepted version of a paper published in Proceedings of the 38th AAAI Conference on Artificial Intelligence is made available via the University of Sheffield Research Publications and Copyright Policy under the terms of the Creative Commons Attribution 4.0 International License (CC-BY 4.0), which permits unrestricted use, distribution and reproduction in any medium, provided the original work is properly cited. To view a copy of this licence, visit [http://creativecommons.org/licenses/by/4.0/](http://creativecommons.org/licenses/by/4.0/)  \nReuse  \nThis article is distributed under the terms of the Creative Commons Attribution (CC BY) licence. This licence allows you to distribute, remix, tweak, and build upon the work, even commercially, as long as you credit the authors for the original work. More information and the full terms of the licence here: [https://creativecommons.org/licenses/](https://creativecommons.org/licenses/)  \nTakedown  \nIf you consider content in White Rose Research Online to be in breach of UK law, please notify us by  \nemailing [eprints@whiterose.ac.uk](eprints@whiterose.ac.uk) including the URL of the record and the reason for the withdrawal request.  \n[eprints@whiterose.ac.uk](eprints@whiterose.ac.uk)[ ](eprints@whiterose.ac.uk)[https://eprints.whiterose.ac.uk/](https://eprints.whiterose.ac.uk/)  \nGeneralization Analysis of Machine Learning Algorithms via the Worst-Case  \nData-Generating Probability Measure  \nXinying Zou 1 , Samir M. Perlaza 1, 2, 3 , I˜naki Esnaola2, 4 , and Eitan Altman 1, 5  \n1 INRIA, Centre Inria d’Universit´e Cˆote d’Azur, Sophia Antipolis 06902, France  \n2Department of Electrical and Computer Engineering, Princeton University, Princeton NJ 08544, USA  \n3 GAATI Laboratory, Universit´e de la Polyn´esie Franc¸aise, Faaa 98702, French Polynesia  \n4Department of Automatic Control and Systems Engineering, University of Shef􀀂eld, Shef􀀂eld S1 3JD, UK  \n5Laboratoire d’Informatique d’Avignon, Universit´e d’Avignon, France  \nxinying.zou@inria.fr, samir.perlaza@inria.fr, esnaola@shef􀀂eld.ac.uk, eitan.altman@inria.fr  \nAbstract  \nIn this paper, the worst-case probability measure over the data is introduced as a tool for characterizing the generalization capabilities of machine learning algorithms. More speci􀀂 -cally, the worst-case probability measure is a Gibbs probability measure and the unique solution to the maximization of the expected loss under a relative entropy constraint with respect to a reference probability measure. Fundamental generalization metrics, such as the sensitivity of the expected loss, the sensitivity of the empirical risk, and the generalization gap are shown to have closed-form expressions involving the worst-case data-generating probability measure. Existing results for the Gibbs algorithm, such as characterizing the generalization gap as a sum of mutual information and lautum information, up to a constant factor, are recovered. A novel parallel is established between the worst-ca","cbCaibc0tPPSQE0s","https://ap.wps.com/l/cbCaibc0tPPSQE0s","pdf",202694,"English","# Abstract\n# 1 Introduction\n# Related Works","[{\"question\":\"What tool does the paper introduce to study generalization of machine learning algorithms?\",\"answer\":\"It introduces the worst-case probability measure over the data to characterize machine learning generalization capabilities.\"},{\"question\":\"How is the worst-case probability measure defined?\",\"answer\":\"It is identified as a Gibbs probability measure and is the unique solution to maximizing the expected loss under a relative-entropy constraint relative to a reference probability measure.\"},{\"question\":\"Which generalization metrics are given closed-form expressions?\",\"answer\":\"The paper provides closed-form expressions for the sensitivity of the expected loss, the sensitivity of the empirical risk, and the generalization gap, all involving the worst-case data-generating probability measure.\"}]","Generalization Analysis of Machine Learning Algorithms via the Worst-Case Data-Generating Probability Measure | PDF",25]