[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-122832-en":3,"doc-seo-122832-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},122832,4810365810221,"Aurora","https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d",8,"Research & Report","Generalization Analysis of Machine Learning Algorithms via the Worst-Case Data-Generating Probability Measure - Accepted Proceedings Paper","The worst-case probability measure over the data is developed as an analytical tool to characterize machine learning generalization. It is formulated as a Gibbs probability measure obtained as the unique optimizer of an expected-loss maximization problem under a relative-entropy constraint to a reference distribution. Closed-form generalization metrics are derived, including sensitivities of expected loss and empirical risk and the generalization gap. Connections to Gibbs-algorithm results are recovered and a shared structure between the model space and data space is identified through this worst-case measure.","[eprints@whiterose.ac.uk](eprints@whiterose.ac.uk)[ ](eprints@whiterose.ac.uk)[https://eprints.whiterose.ac.uk](https://eprints.whiterose.ac.uk)  \nUniversities of Leeds, Sheffield and York  \nDeposited via The University of Sheffield.  \nWhite Rose Research Online URL for this paper:  \n[https://eprints.whiterose.ac.uk/id/eprint/209027/](https://eprints.whiterose.ac.uk/id/eprint/209027/)  \n[Version: Accepted Version](Version: Accepted Version)  \nProceedings Paper:  \nZou, X. , Perlaza, S.M. , Esnaola, J. et al. (2024) Generalization analysis of machine learning algorithms via the worst-case data-generating probability measure. In:  \nProceedings 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. ISSN: 2159-5399. EISSN: 2374-3468.  \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.  \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’UniversitÂe Cˆote d’Azur, Sophia Antipolis 06902, France  \n2Department of Electrical and Computer Engineering, Princeton University, Princeton NJ 08544, USA  \n3 GAATI Laboratory, UniversitÂe de la PolynÂesie FrancËaise, Faaa 98702, French Polynesia  \n4Department of Automatic Control and Systems Engineering, University of Sheffield, Sheffield S1 3JD, UK  \n5Laboratoire d’Informatique d’Avignon, UniversitÂe d’Avignon, France  \nxinying.zou@inria.fr, samir.perlaza@inria.fr, esnaola@sheffield.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 specifically, 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-case data-generating probability measure and the Gibbs algorithm. Specifical","cbCaid9ykr8tVk76","https://ap.wps.com/l/cbCaid9ykr8tVk76","pdf",300232,1,10,"English","en",105,"# Abstract\n# 1 Introduction\n## Expected generalization error and definitions\n## Closed-form results for specific Gibbs settings\n# Related Works","[{\"question\":\"What is the worst-case data-generating probability measure used for?\",\"answer\":\"It is introduced to characterize the generalization capabilities of machine learning algorithms by describing how the worst-case distribution over data influences expected loss and related generalization quantities.\"},{\"question\":\"How is the worst-case probability measure defined in the paper?\",\"answer\":\"It is specified as a Gibbs probability measure, uniquely solving a maximization of expected loss subject to a relative-entropy constraint with respect to a reference probability measure.\"},{\"question\":\"What generalization metrics does the paper derive in closed form?\",\"answer\":\"It provides closed-form expressions for metrics including the sensitivity of the expected loss, the sensitivity of the empirical risk, and the generalization gap, expressed in terms of the worst-case data-generating probability measure.\"}]","Generalization Analysis of Machine Learning Algorithms via the Worst-Case Data-Generating Probability Measure - 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