[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-272059-105":59,"doc-detail-272059-en":131},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":124,"head_meta":126,"extra_data":128,"updated_unix":130},105,"en","justicia-stochastic-sat-approach-to-formally-verify-fairness","Justicia - Stochastic SAT Approach to Formally Verify Fairness","","Machine learning systems can produce socially harmful effects because they do not inherently account for human values, driving the need for formal fairness guarantees. Given many fairness definitions and algorithms, formal verification becomes essential to confirm which fairness metrics hold on specific datasets. This paper proposes Justicia, a stochastic satisfiability framework that verifies fairness measures of supervised learning against the underlying data distribution, including disparate impact, statistical parity, and equalized odds.",{"@graph":69,"@context":123},[70,84,106],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/justicia-stochastic-sat-approach-to-formally-verify-fairness/272059/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/justicia-stochastic-sat-approach-to-formally-verify-fairness/272059.png","ImageObject",300,407,{"name":92,"@type":93},"Gelato","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-01","2026-09-15",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",11,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What problem does Justicia address in fair machine learning?","Question",{"text":113,"@type":114},"Justicia addresses the need to formally verify whether specific fairness metrics are satisfied by supervised learning algorithms on datasets, rather than relying on ad-hoc evaluation.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"Which fairness metrics does the paper target?",{"text":118,"@type":114},"It verifies fairness metrics such as disparate impact, statistical parity, and equalized odds.",{"name":120,"@type":111,"acceptedAnswer":121},"How does Justicia differ from existing distribution-based verifiers?",{"text":122,"@type":114},"Justicia is described as scalable and capable of handling non-Boolean and compound sensitive attributes, and it is more robust than verifiers that operate on specific test samples.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},272059,1790183567,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":52,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":144,"read_time":145,"preview_page_count":4},19241457091524,"https://us-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c","Justicia: A Stochastic SAT Approach to Formally Verify Fairness *  \nBishwamittra Ghosh 1 , Debabrota Basu2,3 , Kuldeep S. Meel 1  \n1 National University of Singapore, Singapore  \n2 Chalmers University of Technology, Gteborg, Sweden  \n3 Scool, Inria Lille-Nord Europe, France  \nAbstract  \nAs a technology ML is oblivious to societal good or bad, and thus, the field of fair machine learning has stepped up to propose multiple mathematical definitions, algorithms, and systems to ensure different notions of fairness in ML applications. Given the multitude of propositions, it has become imperative to formally verify the fairness metrics satisfied by different algorithms on different datasets. In this paper, we propose a stochastic satisfiability (SSAT) framework, Justicia, that formally verifies different fairness measures of supervised learning algorithms with respect to the underlying data distribution. We instantiate Justicia on multiple classification and bias mitigation algorithms, and datasets to verify different fairness metrics, such as disparate impact, statistical parity, and equalized odds. Justicia is scalable, accurate, and operates on non-Boolean and compound sensitive attributes unlike existing distribution-based verifiers, such as FairSquare and VeriFair. Being distribution-based by design, Justicia is more robust than the verifiers, such as AIF360, that operate on specific test samples. We also theoretically bound the finite-sample error of the verified fairness measure.  \n1 Introduction  \nMachine learning (ML) is becoming the omnipresent technology of our time. ML algorithms are being used for highstake decisions like college admissions, crime recidivism, insurance, and loan decisions. Thus, human lives are now pervasively influenced by data, ML, and their inherent bias.  \nExample 1.1. Let us consider an example (Figure 1) of deciding eligibility for health insurance depending on the fitness and income of the individuals of different age groups (20- 40 and 40-60) . Typically, incomes of individuals increase as their ages increase while their fitness deteriorates. We assume relation of income and fitness depends on the age as per the Normal distributions in Figure 1 . Now, if we train a decision tree (Narodytska et al. 2018) on these fitness and income indicators to decide the eligibility of an individual to get a health insurance, we observe that the `optimal' decision tree (ref. Figure 1) selects a person above and below 40 years with probabilities 0:18 and 0:72 respectively. This simple example demonstrates that even if an ML algorithm does not explicitly  \n* Source code: [https://github.com/meelgroup/justicia](https://github.com/meelgroup/justicia)[ ](https://github.com/meelgroup/justicia)Copyright © 2021, Association for the Advancement of Artificial Intelligence ([www.aaai.org](www.aaai.org)). All rights reserved.  \nFigure 1: A trained decision tree to learn eligibility for health insurance using age-dependent fitness and income indicators. learn to differentiate on the basis of a sensitive attribute, it discriminates different age groups due to the utilitarian sense of accuracy that it tries to optimize.  \nFair ML. Statistical discriminations caused by ML algorithms have motivated researchers to develop several frameworks to ensure fairness and several algorithms to mitigate bias. Existing fairness metrics mostly belong to three categories: independence, separation, and sufficiency (Mehrabi et al. 2019) . Independence metrics, such as demographic parity, statistical parity, and group parity, try and ensure the outcomes of an algorithm to be independent of the groups that the individuals belong to (Feldman et al. 2015; Dwork et al. 2012) . Separation metrics, such as equalized odds, define an algorithm to be fair if the probability of getting the same outcomes for different groups are same (Hardt, Price, and Srebro 2016) . Sufficiency metrics, such as counterfactual fairness, constrain the probability of outcomes to be independent o","cbCaiaZqDAxgCeVk","https://ap.wps.com/l/cbCaiaZqDAxgCeVk","pdf",413185,"English","# Introduction\n## Fair ML and fairness metrics\n## Fairness verification frameworks\n## Distributional vs. scalable verification","[{\"question\":\"What problem does Justicia address in fair machine learning?\",\"answer\":\"Justicia addresses the need to formally verify whether specific fairness metrics are satisfied by supervised learning algorithms on datasets, rather than relying on ad-hoc evaluation.\"},{\"question\":\"Which fairness metrics does the paper target?\",\"answer\":\"It verifies fairness metrics such as disparate impact, statistical parity, and equalized odds.\"},{\"question\":\"How does Justicia differ from existing distribution-based verifiers?\",\"answer\":\"Justicia is described as scalable and capable of handling non-Boolean and compound sensitive attributes, and it is more robust than verifiers that operate on specific test samples.\"}]","Justicia - Stochastic SAT Approach to Formally Verify Fairness | PDF",1789462968,25]