[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-120000-en":3,"doc-seo-120000-105":30,"detail-sidebar-cat-0-en-105":95},{"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":20,"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},120000,137441390410,"Hazel","https://ap-avatar.wpscdn.com/avatar/2000252f4ab5702993?_k=1776741390130283984",8,"Research & Report","Fairness in Machine Learning via Optimal Transport","As machine learning decision-making grows in importance, achieving fairness in underlying data processing becomes essential. This dissertation applies optimal transport to deliver provably reliable solutions to key fair ML challenges: statistical parity via Wasserstein pseudo-barycenter and Pareto-frontier characterization; compatibility analysis between group and individual fairness through Pareto trade-offs and individual-fair post-processing guarantees; and equalized odds via conditional Wasserstein barycenter under mild assumptions.","UC Davis  \nUC Davis Electronic Theses and Dissertations  \nTitle  \nFairness in Machine Learning via Optimal Transport  \nPermalink  \n[https://escholarship.org/uc/item/8s79k0qs](https://escholarship.org/uc/item/8s79k0qs)  \nAuthor  \nXu, Shizhou  \nPublication Date  \n2024  \nPeer reviewed|Thesis/dissertation  \n[eScholarship.org](eScholarship.org) Powered by the California Digital Library  \nUniversity of California  \nFairness in Machine Learning via Optimal Transport  \nBy  \nShizhou Xu  \nDISSERTATION  \nSubmitted in partial satisfaction of the requirements for the degree of DOCTOR OF PHILOSOPHY  \nin  \nAPPLIED MATHEMATICS  \nin the  \nOFFICE OF GRADUATE STUDIES  \nof the  \nUNIVERSITY OF CALIFORNIA  \nDAVIS  \nApproved:  \n\n| Naoki Saito |\n| --- |\n| Thomas Strohmer (Chair) |\n\nQinglan Xia Committee in Charge 2024  \n© Shizhou Xu, 2024 . All rights reserved.  \nTo my wife Yuan Ni,  \nmy parents Gang Xu & Jianfeng Ni.  \nii  \nContents  \nAbstract v  \nAcknowledgments vi  \nChapter 1 . Introduction 1  \n1.1. Fairness in Machine Learning 1  \n1.2. Optimization Problems with Sensitive Variable Independence Constraint 5  \n1.3. Challenges in Machine Learning Fairness 8  \n1.4. Corresponding Contributions in Machine Learning Fairness 11  \n1.5. Setting and Notation 15  \n1.6. Dissertation Organization 17  \nChapter 2 . Preliminaries: Optimal Transport 19  \n2.1. General Distribution Case 19  \n2.2. Location-Scale Case and Optimal Affine Transport 24  \nChapter 3 . Pareto Frontier for L2-objective Machine Learning 27  \n3.1. Wasserstein Barycenter Characterization of Optimal Fair Learning 27  \n3.2. Optimal Affine Estimation of Barycenter 30  \n3.3. Wasserstein Geodesics Characterization of Pareto Frontier 36  \nChapter 4 . Fair Data Representation for Conditional Expectation Estimation 47  \n4.1. Objective & Constraint for Fair Data Representation 47  \n4.2. Wasserstein Barycenter Pair Characterization 53  \n4.3. Gaussian Marginals: Exact Solution 57  \n4.4. General Distribution: Optimal Affine Estimation 61  \n4.5. Optimal Fair Data Representation at the Pareto Frontier 66  \n4.6. Algorithm Design 68  \n4.7. Empirical Study: Fair Supervised Learning 71  \nChapter 5 . (In)Compatibility between Group and Individual Fairness 82  \n5.1. Generalized Individual Fairness Definitions 83  \n5.2. Problem Setting 86  \n5.3. Preliminaries on the (Pareto) Optimal Fair L2 Learning 93  \n5.4. Compatibility between the Optimal Statistical Parity L2 Learning and Individual Fairness 96  \n5.5. Compatibility between Pareto Frontier and (ϵ,δ)-IF 99  \n5.6. Composition Results 102  \n5.7. Empirical Study: Group and Individual Fair Supervised Learning 107  \nChapter 6 . Equalized Odds 116  \n6.1. Problem Setting 116  \n6.2. Solution via Conditional Wasserstein Barycenter 119  \nChapter 7 . Future Plan 124  \n7.1. Future Plan on Machine Learning Fairness 124  \n7.2. Future Plan in Broader Directions 125  \nBibliography 127  \nAbstract  \nAs machine learning powered decision-making becomes increasingly important in our daily lives, it is imperative to strive for fairness of the underlying data processing. In this work, we apply optimal transport technique to develop provably trustworthy solutions to open challenges in fair machine learning:  \n• (Statistical parity) We first apply the optimal affine transport to approach the post-processing Wasserstein barycenter characterization of the optimal fair L2-objective supervised learning via a pre-processing data deformation. We call it Wasserstein pseudo-barycenter. Then, we prove that the Wasserstein geodesics from learning outcome marginals to their barycenter characterizes the Pareto frontier between L2-loss and total Wasserstein distance among the marginals. Thereby, an application of McCann interpolation generalizes the pseudo-barycenter to a family of data representations via which L2-objective supervised learning algorithms estimate the Pareto frontier. Numerical simulations underscore the advantages: composition flexibility, sensitive information protection, computat","cbCaiixFXhteceds","https://ap.wps.com/l/cbCaiixFXhteceds","pdf",9790302,1,139,"English","en",105,"# Abstract\n# Chapter 1. Introduction\n## Fairness in Machine Learning\n## Optimization Problems with Sensitive Variable Independence Constraint\n## Challenges in Machine Learning Fairness\n## Corresponding Contributions in Machine Learning Fairness\n## Setting and Notation\n## Dissertation Organization\n# Chapter 2. Preliminaries: Optimal Transport\n## General Distribution Case\n## Location-Scale Case and Optimal Affine Transport\n# Chapter 3. Pareto Frontier for L2-objective Machine Learning\n## Wasserstein Barycenter Characterization of Optimal Fair Learning\n## Optimal Affine Estimation of Barycenter\n## Wasserstein Geodesics Characterization of Pareto Frontier\n# Chapter 4. Fair Data Representation for Conditional Expectation Estimation\n## Objective & Constraint for Fair Data Representation\n## Wasserstein Barycenter Pair Characterization\n## Gaussian Marginals: Exact Solution\n## General Distribution: Optimal Affine Estimation\n## Optimal Fair Data Representation at the Pareto Frontier\n## Algorithm Design\n## Empirical Study: Fair Supervised Learning\n# Chapter 5. (In)Compatibility between Group and Individual Fairness\n## Generalized Individual Fairness Definitions\n## Problem Setting\n## Preliminaries on the (Pareto) Optimal Fair L2 Learning\n## Compatibility between the Optimal Statistical Parity L2 Learning and Individual Fairness\n## Compatibility between Pareto Frontier and (ϵ,δ)-IF\n## Composition Results\n## Empirical Study: Group and Individual Fair Supervised Learning\n# Chapter 6. Equalized Odds\n## Problem Setting\n## Solution via Conditional Wasserstein Barycenter\n# Chapter 7. Future Plan\n## Future Plan on Machine Learning Fairness\n## Future Plan in Broader Directions","[{\"question\":\"How does the dissertation use optimal transport to address fairness in machine learning?\",\"answer\":\"It applies optimal transport to build theoretically grounded methods for fairness, including Wasserstein-based constructions that link fairness objectives to optimization and geometry of distributions.\"},{\"question\":\"What is the role of the Wasserstein barycenter in the statistical-parity results?\",\"answer\":\"The work uses an optimal affine transport approach to form a Wasserstein pseudo-barycenter, then proves connections between Wasserstein geodesics and the Pareto frontier between L2 loss and total Wasserstein distance.\"},{\"question\":\"How are group fairness and individual fairness studied together, and what is the key idea when they conflict?\",\"answer\":\"The dissertation analyzes when optimal statistical parity conflicts with individual fairness, relaxes parity to the Pareto frontier trade-off between L2 error and statistical disparity, and then identifies regions along the frontier that satisfy individual fairness.\"},{\"question\":\"How is equalized odds achieved in this framework?\",\"answer\":\"Equalized odds is characterized through conditional Wasserstein barycenter, yielding solutions under mild assumptions that ensure a broad family of supervised learning models satisfies equalized odds.\"}]","Fairness in Machine Learning via Optimal Transport | 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does the dissertation use optimal transport to address fairness in machine learning?","Question",{"text":75,"@type":76},"It applies optimal transport to build theoretically grounded methods for fairness, including Wasserstein-based constructions that link fairness objectives to optimization and geometry of distributions.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What is the role of the Wasserstein barycenter in the statistical-parity results?",{"text":80,"@type":76},"The work uses an optimal affine transport approach to form a Wasserstein pseudo-barycenter, then proves connections between Wasserstein geodesics and the Pareto frontier between L2 loss and total Wasserstein distance.",{"name":82,"@type":73,"acceptedAnswer":83},"How are group fairness and individual fairness studied together, and what is the key idea when they conflict?",{"text":84,"@type":76},"The dissertation analyzes when optimal statistical parity conflicts with individual fairness, relaxes parity to the Pareto frontier trade-off between L2 error and statistical disparity, and then identifies regions along the frontier that satisfy individual fairness.",{"name":86,"@type":73,"acceptedAnswer":87},"How is equalized odds achieved in this framework?",{"text":88,"@type":76},"Equalized odds is characterized through conditional Wasserstein barycenter, yielding solutions under mild assumptions that ensure a broad family of supervised learning models satisfies equalized odds.","https://schema.org",{"og:url":52,"og:type":91,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":93,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":96},[97,101,105,109,114,119,124,127,132,135,139],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Story & 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