[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-126131-en":3,"doc-seo-126131-105":31,"detail-sidebar-cat-0-en-105":92},{"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":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":28,"seo_description":14,"update_tm":29,"read_time":30},126131,5909887254083,"Miles","https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c",8,"Research & Report","Fair Data Representation for Machine Learning at the Pareto Frontier","As machine learning increasingly drives daily decision-making, ensuring fairness in the underlying data processing becomes essential. The work presents a pre-processing algorithm for fair data representation that connects supervised learning with an L2(P)-objective to estimations of the Pareto frontier between prediction error and statistical disparity. Using optimal affine transport, it links the problem to a post-processing Wasserstein barycenter characterization. Wasserstein geodesics from learning-outcome marginals to their barycenter further describe the Pareto frontier trade-off, while simulations show compositionality, sensitive-information protection, and computational efficiency in high dimensions.","UC Davis  \nUC Davis Previously Published Works  \nTitle  \nFair Data Representation for Machine Learning at the Pareto Frontier.  \nPermalink  \n[https://escholarship.org/uc/item/67z9r23d](https://escholarship.org/uc/item/67z9r23d)  \nAuthors  \nXu, Shizhou  \nStrohmer, Thomas  \nPublication Date  \n2023  \nPeer reviewed  \n[eScholarship.org](eScholarship.org) Powered by the California Digital Library  \nUniversity of California  \nAuthor Manuscript Author Manuscript Author Manuscript Author Manuscript  \n\n|  | HHS Public Access\u003Cbr>Author manuscript\u003Cbr>J Mach Learn Res. Author manuscript; available in PMC 2024 October 22. |\n| --- | --- |\n\nPublished in final edited form as: J Mach Learn Res. 2023 ; 24: .  \nFair Data Representation for Machine Learning at the Pareto Frontier  \nShizhou Xu,  \nDepartment of Mathematics, University of California Davis, Davis, CA 95616-5270, USA  \nThomas Strohmer  \nDepartment of Mathematics, Center of Data Science and Artificial Intelligence Research, University of California Davis, Davis, CA 95616-5270, USA  \nAbstract  \nAs machine learning powered decision-making becomes increasingly important in our daily lives, it is imperative to strive for fairness in the underlying data processing. We propose a  \npre-processing algorithm for fair data representation via which L2(ℙ)-objective supervised learning results in estimations ofthe Pareto frontier between prediction error and statistical disparity.  \nParticularly, the present work applies 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. Furthermore, we show 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. Numerical simulations underscore the advantages: (1) the pre-processing step is compositive with arbitrary conditional expectation estimation supervised learning methods and unseen data; (2) the fair representation protects the sensitive information by limiting the inference capability of the remaining data with respect to the sensitive data; (3) the optimal affine maps are computationally efficient even for high-dimensional data.  \nKeywords  \nstatistical parity; equalized odds; Wasserstein barycenter; Wasserstein geodesics; conditional expectation estimation  \n1. Introduction  \nOur society is increasingly influenced by artificial intelligence as (direct or indirect) decision-making processes become more reliant on statistical inference and machine learning. The potentially significant long-term impact from sequences of automated (facilitate of) decision-making has brought large concerns about bias and discrimination  \nLicense: CC-BY 4.0, see [https://creativecommons.org/licenses/by/4.0/](https://creativecommons.org/licenses/by/4.0/. Attribution requirements)[. Attribution requirements](https://creativecommons.org/licenses/by/4.0/. Attribution requirements) are provided at [http://jmlr.org/](http://jmlr.org/)[ ](http://jmlr.org/)[papers/v/.html](papers/v/.html.)[.](papers/v/.html.)  \nSHZXU@UCDAVIS.EDU .  \nAuthor Manuscript Author Manuscript Author Manuscript Author Manuscript  \nXu and Strohmer Page 2  \nin machine learning [3, 39]. Machine learning based on unbiased algorithms can naturally inherit the historical biases that exist in data and hence reinforce the bias via automated decision-making process [11] .  \nOne straightforward partial remedy is to exclude the sensitive variables from the data set used in the learning and decision process. But such exclusion merely eliminates disparate treatment, which refers to direct discrimination, and leaves disparate impact, which refers to unintended or indirect discrimination, remaining in both data and learning outcome  \n[20] . Examples of the legal doctrine of disparate impact include Griggs v. Duke Powers Co. [32] and Ricci v. DeStefano [33], w","cbCait3MSOWasK9p","https://ap.wps.com/l/cbCait3MSOWasK9p","pdf",3254322,4,1,71,"English","en",105,"# Introduction\n## Group and individual fairness goals\n## Statistical parity and application context\n## Problem motivation and need for practical techniques\n# (Implied) Fair data representation via pre-processing\n## Pareto frontier between L2 loss and statistical disparity\n## Optimal affine transport and Wasserstein barycenter characterization\n# (Implied) Wasserstein geodesics and characterization of trade-offs\n## Learning-outcome marginals to their barycenter","[{\"question\":\"What fairness objective does the work target?\",\"answer\":\"It targets group fairness via statistical parity, which is closely related to disparate impact and long-term structural influence.\"},{\"question\":\"How is fair data representation achieved?\",\"answer\":\"A pre-processing algorithm deforms the data so that supervised learning with an L2(P)-objective yields estimations of the Pareto frontier between prediction error and statistical disparity.\"},{\"question\":\"What do the Wasserstein barycenter and geodesics contribute?\",\"answer\":\"The optimal affine transport approach links the optimal fair L2 supervised learning to a Wasserstein barycenter post-processing characterization, and Wasserstein geodesics from outcome marginals to the barycenter describe the Pareto frontier between L2-loss and Wasserstein distances among marginals.\"}]","Fair Data Representation for Machine Learning at the Pareto Frontier | 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fairness objective does the work target?","Question",{"text":76,"@type":77},"It targets group fairness via statistical parity, which is closely related to disparate impact and long-term structural influence.","Answer",{"name":79,"@type":74,"acceptedAnswer":80},"How is fair data representation achieved?",{"text":81,"@type":77},"A pre-processing algorithm deforms the data so that supervised learning with an L2(P)-objective yields estimations of the Pareto frontier between prediction error and statistical disparity.",{"name":83,"@type":74,"acceptedAnswer":84},"What do the Wasserstein barycenter and geodesics contribute?",{"text":85,"@type":77},"The optimal affine transport approach links the optimal fair L2 supervised learning to a Wasserstein barycenter post-processing characterization, and Wasserstein geodesics from outcome marginals to the barycenter describe the Pareto frontier between L2-loss and Wasserstein distances among 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