[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-86378-en":3,"doc-seo-86378-105":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":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":13,"seo_description":14,"update_tm":28,"read_time":29},86378,34359740700684,"Finn","https://ap-avatar.wpscdn.com/avatar/1f400023980c374ae676?_k=1777273430885731487",8,"Research & Report","Separation-Utility Pareto Frontier An Information Theoretic Characterization","Study of the Pareto frontier between predictive utility and separation, where separation requires predictive independence from sensitive attributes conditioned on the true outcome. The work characterizes the achievable separation–utility region using information theory, proves that the revealed randomized frontier equals the concave closure of the deterministic frontier, and analyzes how the separation cost changes along the trade-off. It derives conditions for strict trade-offs and proposes a CMI-based empirical regularizer that directly estimates conditional mutual information from samples, avoiding adversarial proxies. Experiments on multiple benchmarks validate stable frontiers and strong low-violation performance.","arXiv :2602 .04408v 3 [ cs .LG] 13 Jul 2026  \nSeparation-Utility Pareto Frontier:  \nAn Information-Theoretic Characterization  \nShizhou Xu  \nDepartment of Mathematics  \nUniversity of California Davis  \nDavis, CA 95616, USA  \nAbstract  \nWe study the Pareto frontier between predictive utility and separation, a fairness criterion requiring predictive independence from sensitive attributes conditional on the true outcome.  \nThrough an information-theoretic lens, we characterize the achievable separation–utility region, prove that the revealed randomized frontier is the concave closure of the deterministic frontier, and clarify how the marginal cost of separation varies along the frontier. We further identify sufficient conditions under which the trade-off is strict, providing theoretical guidance for interpreting empirical frontiers and choosing operating points. Motivated by this characterization, we develop a direct empirical regularizer based on conditional mutual information (CMI) for discrete target and sensitive variables. By estimating CMI directly from sample statistics, the resulting plug-in regularizer avoids reliance on adversarial or variational proxy losses, is compatible with deep models trained by gradient-based optimization, and provides a scalar monitor of residual separation violation with finite-sample guarantees.  \nExperiments on COMPAS, UCI Adult, UCI Bank, CelebA, and ACS show that the proposed method traces stable separation-utility frontiers, substantially reduces separation violations, and achieves competitive trade-offs relative to established baselines, often improving the low-violation region. This study offers a principled, stable, and flexible framework for navigating separation–utility trade-offs in deep learning.  \n1 Introduction  \nAutomated decision systems are increasingly deployed in high-stakes domains such as finance, criminal justice, hiring, and healthcare, making verifiable fairness constraints an essential component of reliable machine learning [3] . A central challenge is that fairness criteria often conflict with model utility [9; 20], creating a critical need for a framework that provides practitioners with a provably optimal and practically implementable trade-off.  \nIn this work, we focus on separation (or equalized odds in binary classification), which requires conditional independence between the model output  and a sensitive attribute Z given the true label Y [16]:  \n ⊥ Z | Y.  \nAny dependence of  on Z must be justified by the overlapping information between Z and the target Y. Separation is particularly relevant when base rates differ across groups, as it rules out unjustified group-dependent errors while remaining compatible with perfect prediction. 1  \nInformation-plane view and the Pareto frontier. We take an information-theoretic perspective on the separation-utility trade-off by quantifying (i) separation violation v by the conditional mutual information  \n1We adopt separation as the fairness definition throughout. Comparing separation to alternative notions (e.g. , independence, calibration) is beyond the scope of this paper.  \n(CMI), and (ii) predictive utility u by mutual information (MI):  \nv () := I (; Z | Y ), u () := I (; Y ) .  \nHere, v characterizes separation at v () = 0, whereas u is equivalent to minimizing the Bayes-optimal conditional log-loss, yields Fano-type necessary conditions for small classification error in finite-label settings, and connects to general distortion losses through rate-distortion theory [13] .  \nNovelty relative to prior CMI-based fairness work. While the equivalence I (; Z | Y ) = 0 ⇐⇒  ⊥ Z | Y follows directly from the definition of conditional mutual information, our contributions are (i) a population-level characterization of the achievable separation-utility region and the optimal randomized Pareto frontier, showing that revealed randomization is necessary in general and that mixing between at most two deterministic predictors suffices","cbCaigzWOezbuMNg","https://ap.wps.com/l/cbCaigzWOezbuMNg","pdf",1894130,4,1,48,"English","en",105,"# Introduction\n## Information-plane view and the Pareto frontier\n## Novelty relative to prior CMI-based fairness work\n## From theory to practice: An empirical regularizer\n## Related Works","[{\"question\":\"What does the paper define as the fairness criterion separation?\",\"answer\":\"Separation requires conditional independence between the model output and a sensitive attribute Z given the true label Y. Dependence on Z is only allowed if it is justified by overlapping information between Z and Y.\"},{\"question\":\"How is the separation–utility trade-off quantified in the paper?\",\"answer\":\"Separation violation is measured by conditional mutual information I(Ŷ; Z | Y), while predictive utility is measured by mutual information I(Ŷ; Y). These two quantities form an information-plane feasibility region and its Pareto frontier.\"},{\"question\":\"What empirical method does the paper introduce to enforce separation?\",\"answer\":\"The paper proposes a direct in-processing regularizer based on an empirical plug-in estimator of conditional mutual information. This avoids adversarial or variational proxy losses and provides a scalar monitor of residual separation violation with finite-sample guarantees.\"}]",1784211291,121,{"code":4,"msg":31,"data":32},"ok",{"site_id":25,"language":24,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"separation-utility-pareto-frontier-an-information-theoretic-characterization","",{"@graph":36,"@context":85},[37,53,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":21},"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":20},"https://docshare.wps.com/document/separation-utility-pareto-frontier-an-information-theoretic-characterization/86378/",{"url":52,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":24,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":41,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-27","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What does the paper define as the fairness criterion separation?","Question",{"text":75,"@type":76},"Separation requires conditional independence between the model output and a sensitive attribute Z given the true label Y. Dependence on Z is only allowed if it is justified by overlapping information between Z and Y.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How is the separation–utility trade-off quantified in the paper?",{"text":80,"@type":76},"Separation violation is measured by conditional mutual information I(Ŷ; Z | Y), while predictive utility is measured by mutual information I(Ŷ; Y). These two quantities form an information-plane feasibility region and its Pareto frontier.",{"name":82,"@type":73,"acceptedAnswer":83},"What empirical method does the paper introduce to enforce separation?",{"text":84,"@type":76},"The paper proposes a direct in-processing regularizer based on an empirical plug-in estimator of conditional mutual information. This avoids adversarial or variational proxy losses and provides a scalar monitor of residual separation violation with finite-sample guarantees.","https://schema.org",{"og:url":52,"og:type":87,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":89,"canonical":52},"index,follow",{"doc_id":7,"site_id":25},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,123,128,131,135],{"id":21,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":20,"doc_module":4,"doc_module_name":46,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":46,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":46,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":132,"doc_module":4,"doc_module_name":46,"category_name":133,"show_sort_weight":132,"slug":134},10,"Lifestyle","lifestyle",{"id":136,"doc_module":4,"doc_module_name":46,"category_name":137,"show_sort_weight":106,"slug":138},19,"General","general"]