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Fairness verification aims to detect and quantify bias against demographic groups by reasoning over feature probability distributions beyond finite datasets. For linear classifiers, prior approaches can suffer accuracy loss from imprecise feature-correlation modeling and poor scalability due to restrictive SSAT/SMT encodings or sampling. This work introduces FVGM, encoding correlations via Bayesian networks and using a stochastic subset-sum method to enable accurate, scalable fairness evaluation and analysis.",{"@graph":69,"@context":122},[70,84,105],{"@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/algorithmic-fairness-verification-with-graphical-models-paper/272564/",{"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/algorithmic-fairness-verification-with-graphical-models-paper/272564.png","ImageObject",300,407,{"name":92,"@type":93},"Ben Jamin","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-17","2026-09-15",true,{"@type":102,"interactionType":103,"userInteractionCount":39},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What problem does the paper address?","Question",{"text":112,"@type":113},"The paper addresses fairness verification for machine learning classifiers, especially linear classifiers, when inputs follow probability distributions rather than a finite dataset.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How does FVGM differ from prior fairness verifiers?",{"text":117,"@type":113},"FVGM encodes feature correlations using a Bayesian network and verifies linear classifiers using a stochastic subset-sum approach instead of relying on SSAT/SMT encodings or sampling-heavy methods.",{"name":119,"@type":110,"acceptedAnswer":120},"Which fairness definitions are examined?",{"text":121,"@type":113},"The paper focuses on two families of fairness definitions: group fairness metrics and causal fairness metrics.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},272564,1789466102,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":39,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":44,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":129,"read_time":143,"preview_page_count":4},2336478466772,"https://ap-avatar.wpscdn.com/davatar_3d24733baf745e90a7e4bdd5f77d97b2","Algorithmic Fairness Verification with Graphical Models*  \nBishwamittra Ghosh, 1 Debabrota Basu,2 Kuldeep S. Meel 1  \n1 School of Computing, National University of Singapore, Singapore  \n2 ´Equipe Scool, Univ. Lille, Inria, UMR 9189-CRIStAL, CNRS, Centrale Lille, France  \nAbstract  \nIn recent years, machine learning (ML) algorithms have been deployed in safety-critical and high-stake decision-making, where the fairness of algorithms is of paramount importance. Fairness in ML centers on detecting bias towards certain demographic populations induced by an ML classifier and proposes algorithmic solutions to mitigate the bias with respect to different fairness definitions. To this end, several fairness verifiers have been proposed that compute the bias in the prediction of an ML classifier—essentially beyond a finite dataset—given the probability distribution of input features. In the context of verifying linear classifiers, existing fairness verifiers are limited by accuracy due to imprecise modeling of correlations among features and scalability due to restrictive formulations of the classifiers as SSAT/SMT formulas or by sampling. In this paper, we propose an efficient fairness verifier, called FVGM, that encodes the correlations among features as a Bayesian network. In contrast to existing verifiers, FVGM proposes a stochastic subset-sum based approach for verifying linear classifiers. Experimentally, we show that FVGM leads to an accurate and scalable assessment for more diverse families of fairness-enhancing algorithms, fairness attacks, and group/causal fairness metrics than the state-of-the-art. We also demonstrate that FVGM facilitates the computation of fairness influence functions as a stepping stone to detect the source of bias induced by subsets of features.  \n1 Introduction  \nThe significant improvement of machine learning (ML) over the decades has led to a host of applications of ML in high-stake decision-making such as college admission (Martinez Neda, Zeng, and Gago-Masague 2021), hiring of employees (Ajunwa et al. 2016), and recidivism prediction (Tollenaar and Van der Heijden 2013; Dressel and Farid 2018) . ML algorithms often have an accuracy-centric learning objective, which may cause them to be biased towards certain part of the dataset belonging to a certain economically or socially sensitive groups (Landy, Barnes, and Murphy 1978; Zliobaite 2015; Berk 2019) . The following example illustrates a plausible case of unfairness induced by ML algorithms. Example 1.1. Following (Ghosh, Basu, and Meel 2021, Example 1. ), let us consider an ML problem where the classifier  \n* Source code: [https://github.com/meelgroup/justicia](https://github.com/meelgroup/justicia)[ ](https://github.com/meelgroup/justicia)Copyright © 2022, Association for the Advancement of Artificial Intelligence ([www.aaai.org](www.aaai.org)). All rights reserved.  \ndecides the eligibility of an individual for health insurance given their income and fitness (Figure 1) . Here, the sensitive feature `age' (A) follows a Bernoulli distribution, and income (I) and fitness (F ) follow Gaussian distributions. We generate 1000 samples from these distributions and use them to train a Support Vector Machine (SVM) classifier. The decision boundary of this classifier is 9:37I + 9:75F 􀀀 0:34A 􀀕 9:4, where A = 1 denotes the sensitive group `age 􀀕 40'. This classifier selects an individual above and below 40 years of age with probabilities 0:24 and 0:86, respectively. This illustrates a disparate treatment of individuals of two age groups by the SVM classifier.  \n~~ ~~ age \u003C 40 ~~ ~~ age  40  \n0.0 0.5 income  \n1.0 0.0 0.5 1.0  \nfitness  \nFigure 1: Age-dependent distributions of income and fitness in Example 1.1 .  \nIn order to identify and mitigate the bias of ML classifiers, different fairness definitions and fairness algorithms have been proposed (Hardt, Price, and Srebro 2016; Kusner et al. 2017; Mehrabi et al. 2019) . In this paper, we focus on two families of fairness definitions: g","cbCaitU7XpPOGtnQ","https://ap.wps.com/l/cbCaitU7XpPOGtnQ","pdf",493951,"English","# Introduction\n## Fairness in high-stakes ML\n## Fairness verification problem\n## Fairness definitions: group vs causal fairness\n## Limitations of existing verifiers","[{\"question\":\"What problem does the paper address?\",\"answer\":\"The paper addresses fairness verification for machine learning classifiers, especially linear classifiers, when inputs follow probability distributions rather than a finite dataset.\"},{\"question\":\"How does FVGM differ from prior fairness verifiers?\",\"answer\":\"FVGM encodes feature correlations using a Bayesian network and verifies linear classifiers using a stochastic subset-sum approach instead of relying on SSAT/SMT encodings or sampling-heavy methods.\"},{\"question\":\"Which fairness definitions are examined?\",\"answer\":\"The paper focuses on two families of fairness definitions: group fairness metrics and causal fairness metrics.\"}]","Algorithmic Fairness Verification with Graphical Models - Paper | PDF",23]