[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-117440-en":3,"doc-seo-117440-105":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},117440,13056703019404,"Miles","https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0",8,"Research & Report","Fairness and Foundations of Machine Learning - Thesis dissertation","This dissertation investigates fairness and theoretical foundations in machine learning. It analyzes benign overfitting, showing that models can achieve perfect accuracy on noisy training data while maintaining asymptotically optimal generalization. The work studies shallow ReLU networks and leaky ReLU networks under multiple hyperparameter regimes, identifying benign, non-benign, and no-overfitting behaviors. It further studies fairness through subgroup-aware linear regression via a Kaczmarz variation, and group-unequal performance in non-negative matrix factorization. A new NMF loss and algorithms reduce disparities using a fairness metric. Finally, it formalizes observational multiplicity through regret quantifying non-uniform prediction arbitrariness across populations.","UCLA  \nUCLA Electronic Theses and Dissertations  \nTitle  \nFairness and Foundations of Machine Learning  \nPermalink  \n[https://escholarship.org/uc/item/1qb8k234](https://escholarship.org/uc/item/1qb8k234)  \nAuthor  \nGeorge, Erin Wise  \nPublication Date  \n2025  \nPeer reviewed|Thesis/dissertation  \n[eScholarship.org](eScholarship.org) Powered by the California Digital Library  \nUniversity of California  \nUNIVERSITY OF CALIFORNIA Los Angeles  \nFairness and Foundations of Machine Learning  \nA dissertation submitted in partial satisfaction of the requirements for the degree Doctor of Philosophy in Mathematics  \nby  \nErin Wise George  \n2025  \n© Copyright by Erin Wise George 2025  \nABSTRACT OF THE DISSERTATION  \nFairness and Foundations of Machine Learning  \nby  \nErin Wise George  \nDoctor of Philosophy in Mathematics  \nUniversity of California, Los Angeles, 2025  \nProfessor Deanna Needell, Chair  \nIn this dissertation, we study fairness and foundations in machine learning tasks. In the first part, we study the theory of benign overfitting, where machine learning models are capable of attaining perfect accuracy on noisy training data while still obtaining asymptotically optimal generalization performance. We extend results in a standard high-dimensional setting to apply to shallow (single-hidden-layer) ReLU neural networks trained with hinge loss and prove that, under three different regimes of hyperparameters, three different phenomena occur: benign overfitting, non-benign overfitting, and no overfitting. We then study a much lower-dimensional setting for leaky ReLU neural networks with hinge loss and prove that, under two different regimes of hyperparameters, two different phenomena occur: benign and non-benign overfitting. We then switch to studying the fairness of machine learning models. First, we study a variation of the Kaczmarz method for linear regression that works in the case there are subgroups within the data with unknown membership that each exhibit a different linear relationship between features and labels. We prove convergence results for our new method and demonstrate experimentally that these results hold. We then study non-negative matrix factorization (NMF) and show that NMF can result in reconstructions that have unequal performance across groups in a dataset. We propose a variant of the  \nNMF loss function to solve this problem, detail two different algorithms to find factorizations minimizing this loss, and demonstrate that these factorizations perform better according to our fairness metric. Lastly, we study the concept of observational multiplicity, which captures the “arbitrariness” in machine learning predictions that arises because the predictions are a function of a random data sample. These predictions are arbitrary since a different set of predictions would be obtained from a different random sample, even if the sample is from the same distribution. We show that this can be quantified with a value that we refer to as regret and that, in general, for a fixed machine learning task regret is not uniform across the population of interest.  \nThe dissertation of Erin Wise George is approved.  \nChenfanfu Jiang  \nGuido Francisco Montúfar Cuartas Mason Alexander Porter Deanna Needell, Committee Chair  \nUniversity of California, Los Angeles  \n2025  \nTo Wes.  \nv  \nTABLE OF CONTENTS  \n1 Introduction ...................................... 1  \n2 Benign overfitting in high-dimensional ReLU networks ........... 4  \n2.1 Introduction .................................... 5  \n2.1.1 Contributions and related work ..................... 6  \n2.2 Preliminaries ................................... 9  \n2.2.1 Data model ................................ 9  \n2.2.2 Network architecture, optimization and initialization ......... 10  \n2.2.3 Notation .................................. 11  \n2.3 Results ....................................... 12  \n2.3.1 Benign overfitting ............................. 14  \n2.3.2 Non-benign overfitting .....","cbCaij549FiuSFIo","https://ap.wps.com/l/cbCaij549FiuSFIo","pdf",6619771,1,283,"English","en",105,"# Introduction\n# Benign overfitting in high-dimensional ReLU networks\n## Introduction\n## Contributions and related work\n## Preliminaries\n## Data model\n## Network architecture, optimization and initialization\n## Notation\n## Results\n## Benign overfitting\n## Non-benign overfitting\n## No overfitting\n## Comparison of results\n## Properties of the data and network at initialization\n## Supporting Lemmas\n## Numerical simulations\n## Conclusion\n# Benign overfitting in leaky ReLU networks with moderate input dimension","[{\"question\":\"What does the dissertation mean by “benign overfitting” in machine learning models?\",\"answer\":\"It studies cases where models fit noisy training data with perfect accuracy while still achieving asymptotically optimal generalization performance. The dissertation characterizes when this favorable behavior occurs.\"},{\"question\":\"How does the dissertation treat fairness in learning tasks?\",\"answer\":\"It examines fairness by studying subgroup-aware linear regression with unknown subgroup memberships and by analyzing group disparities produced by non-negative matrix factorization. It then proposes an NMF loss variant aimed at improving fairness under a fairness metric.\"},{\"question\":\"What is observational multiplicity and how is it quantified?\",\"answer\":\"Observational multiplicity captures arbitrariness in predictions caused by using a random data sample. The dissertation quantifies this with a value called regret, showing it generally varies across the population of interest.\"}]","Fairness and Foundations of Machine Learning - Thesis dissertation | PDF",1785675885,713,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"fairness-and-foundations-of-machine-learning-thesis-dissertation","",{"@graph":36,"@context":85},[37,54,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/fairness-and-foundations-of-machine-learning-thesis-dissertation/117440/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":62,"encodingFormat":61,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-02",true,{"@type":65,"interactionType":66,"userInteractionCount":4},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What does the dissertation mean by “benign overfitting” in machine learning models?","Question",{"text":75,"@type":76},"It studies cases where models fit noisy training data with perfect accuracy while still achieving asymptotically optimal generalization performance. The dissertation characterizes when this favorable behavior occurs.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does the dissertation treat fairness in learning tasks?",{"text":80,"@type":76},"It examines fairness by studying subgroup-aware linear regression with unknown subgroup memberships and by analyzing group disparities produced by non-negative matrix factorization. It then proposes an NMF loss variant aimed at improving fairness under a fairness metric.",{"name":82,"@type":73,"acceptedAnswer":83},"What is observational multiplicity and how is it quantified?",{"text":84,"@type":76},"Observational multiplicity captures arbitrariness in predictions caused by using a random data sample. 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