[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-121140-en":3,"doc-seo-121140-105":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":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},121140,1099514068035,"Ezra","https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c",8,"Research & Report","Statistical learning for constrained functional parameters in infinite-dimensional models with applications in fair machine learning","Constrained learning is increasingly central to algorithmic fairness, where predictive models are built to satisfy predefined notions of fair treatment. This study frames constrained statistical machine learning via a statistical functional viewpoint, learning a function-valued parameter while enforcing that one or more specified functional parameters are zero or bounded. The constrained functional parameter is characterized as a minimizer of a penalized risk through a Lagrange multiplier formulation, often yielding closed-form solutions and guiding estimators. The method supports construction of fair learning algorithms across diverse learning approaches and demonstrates broad applicability on multiple fairness constraints.","arXiv :2404 .09847v1 [ stat .ML] 15 Apr 2024  \nStatistical learning for constrained functional parameters in infinite-dimensional models with applications in fair machine learning  \nRazieh Nabi 1 , Nima S. Hejazi2 , Mark J. van der Laan3 , and David Benkeser 1  \n1 Department of Biostatistics and Bioinformatics, Rollins School of Public Health, Emory University, Atlanta, GA, USA  \n2 Department of Biostatistics, T.H. Chan School of Public Health, Harvard University, Boston, MA, USA  \n3 Division of Biostatistics, School of Public Health, University of California, Berkeley, Berkeley, CA, USA  \nAbstract  \nConstrained learning has become increasingly important, especially in the realm of algorithmic fairness and machine learning. In these settings, predictive models are developed specifically to satisfy pre-defined notions of fairness. Here, we study the general problem of constrained statistical machine learning through a statistical functional lens. We consider learning a function-valued parameter of interest under the constraint that one or several pre-specified real-valued functional parameters equal zero or are otherwise bounded. We characterize the constrained functional parameter as the minimizer of a penalized risk criterion using a Lagrange multiplier formulation. We show that closed-form solutions for the optimal constrained parameter are often available, providing insight into mechanisms that drive fairness in predictive models. Our results also suggest natural estimators of the constrained parameter that can be constructed by combining estimates of unconstrained parameters of the data generating distribution. Thus, our estimation procedure for constructing fair machine learning algorithms can be applied in conjunction with any statistical learning approach and off-the-shelf software. We demonstrate the generality of our method by explicitly considering a number of examples of statistical fairness constraints and implementing the approach using several popular learning approaches.  \nKeywords: Constrained learning, Algorithmic fairness, Artificial intelligence, Machine learning, Counterfactual fairness, Causal inference  \n1 Introduction  \nStatistical machine learning algorithms have gained widespread use in automating decisionmaking processes across various domains. The potential benefits of these systems are substantial, with the ability to enhance economic productivity, policy efficiency, and human health. However, there exists a significant risk that these algorithms may perpetuate biases and widen existing societal disparities. Thus, it is crucial to ensure that machine learning models are explicitly designed to exhibit fair decision-making. Recent years have seen a surge of interest in incorporating constraints for predictive and decision support systems to address these issues. The notion of algorithmic fairness focuses on providing a technical understanding of such issues within their relevant social contexts, with the overarching aim of mitigating unfair treatment of individuals based on sensitive characteristics (e.g., gender and/or race/ethnicity) . Many definitions of fairness are available in the literature [Mitchell et al., 2021, Plecko and Bareinboim, 2022, Barocas et al., 2023]; however, there is no consensus on a universal criterion for fair statistical learning. Indeed, there has been debate about the relevance of the various criteria [Prince and Schwarcz, 2019, Kilbertus et al., 2020] and an increasing recognition that it is often impossible to satisfy multiple fairness criteria simultaneously [Kleinberg et al., 2017, Corbett-Davies and Goel, 2018, Friedler et al., 2021] .  \nIrrespective of the fairness criteria adopted, the objective of algorithmic fairness in practice involves using data to create a prediction system that adheres to a user-selected fairness constraint. The literature on constrained learning for fairness can broadly be categorized into three primary categories based on the stage of inter","cbCaieCZjH63PXkP","https://ap.wps.com/l/cbCaieCZjH63PXkP","pdf",1088741,1,80,"English","en",105,"# Introduction\n## Background and motivation\n## Constrained learning categories for fairness\n# Constrained functional learning framework\n## Lagrange multiplier and penalized risk characterization\n## Closed-form solutions and estimators\n# Applications to fair machine learning\n## Fairness constraints and implementation approaches","[{\"question\":\"What problem does the paper address in constrained statistical learning?\",\"answer\":\"It studies constrained statistical machine learning by learning a function-valued parameter subject to functional constraints that are zero or otherwise bounded.\"},{\"question\":\"How is the constrained functional parameter characterized mathematically?\",\"answer\":\"It is characterized as the minimizer of a penalized risk criterion using a Lagrange multiplier formulation.\"},{\"question\":\"How do the proposed results help build fair machine learning algorithms?\",\"answer\":\"The framework provides closed-form insights for the optimal constrained parameter and suggests natural estimators that combine estimates of unconstrained parameters, enabling fair learning with common learning approaches and software.\"}]","Statistical learning for constrained functional parameters in infinite-dimensional models with applications in fair machine learning | 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problem does the paper address in constrained statistical learning?","Question",{"text":75,"@type":76},"It studies constrained statistical machine learning by learning a function-valued parameter subject to functional constraints that are zero or otherwise bounded.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How is the constrained functional parameter characterized mathematically?",{"text":80,"@type":76},"It is characterized as the minimizer of a penalized risk criterion using a Lagrange multiplier formulation.",{"name":82,"@type":73,"acceptedAnswer":83},"How do the proposed results help build fair machine learning algorithms?",{"text":84,"@type":76},"The framework provides closed-form insights for the optimal constrained parameter and suggests natural estimators that combine estimates of unconstrained parameters, enabling fair learning with common learning approaches and 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