[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-82746-en":3,"doc-seo-82746-105":29,"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":13,"seo_description":14,"update_tm":27,"read_time":28},82746,549758252649,"Ivy","https://ap-avatar.wpscdn.com/avatar/8000253669c5317157?_k=1778319167496531819",8,"Research & Report","Towards Diverse and Comprehensive Benchmarks for Mutual Information Estimation","Mutual information estimation is a central challenge in machine learning and statistics, yet existing benchmarks often test estimators only on simplified, low-dimensional distributions, leaving performance on realistic complex data insufficiently understood. This work introduces a comprehensive benchmarking framework built on a unified copula-theoretic viewpoint that generalizes prior benchmarks. Two complementary test families vary ground-truth MI and marginal complexity, evaluate three estimator classes, find no universal winner, and design sharper stress tests. Open-source code is released.","arXiv :2607 .03487v 1 [ cs .LG] 3 Jul 2026  \nTowards Diverse and Comprehensive Benchmarks for Mutual Information Estimation  \nAlberto Foresti∗ Giulio Franzese  \nPietro Michiardi  \nDepartment of Data Science EURECOM  \n450 Route des Chappes, 06410 Biot, France  \nIvan Butakov∗  \nAlexander Tolmachev  \nApplied AI Institute  \nPresnenskaya naberezhnaya, 12, 121205 Moscow, Russia  \n[alberto.foresti@eurecom.fr](alberto.foresti@eurecom.fr)[ ](alberto.foresti@eurecom.fr)[giulio.franzese@eurecom.fr](giulio.franzese@eurecom.fr)[ ](giulio.franzese@eurecom.fr)[pietro.michiardi@eurecom.fr](pietro.michiardi@eurecom.fr)  \n[ivan.butakov@applied-ai. ru](ivan.butakov@applied-ai. ru)[a.tolmachev@applied-ai. ru](a.tolmachev@applied-ai. ru)  \nMoscow Independent Research Institute of Artificial Intelligence  \nBolshaya Cheremushkinskaya Street, 20, Building 4, Premises 3/1, 117218 Moscow, Russia  \nAlexey Frolov [al.frolov@applied-ai. ru](al.frolov@applied-ai. ru)  \nApplied AI Institute  \nPresnenskaya naberezhnaya, 12, 121205 Moscow, Russia  \nAbstract  \nMutual information (MI) estimation is a central problem in machine learning and statistics;  \nhowever, existing benchmarks typically evaluate estimators on simplified, low-dimensional distributions, leaving their performance on complex, realistic data largely unexplored. We address this gap with a comprehensive benchmarking framework grounded in a unified copula-theoretic perspective that subsumes existing benchmarks as special cases. Within this framework, we propose two complementary families of tests: a copula-first family that systematically varies ground-truth MI, dimensionality, and marginal complexity using synthetic and flow-based transformations; and a marginals-first family that couples real-world image data with controlled dependency structures, extending the classic same-class-pairing paradigm. We use this suite to extensively evaluate three classes of estimators: nonparametric, discriminative, and generative. Contrary to prevailing assumptions, our results indicate that there is no universal winner: each category can systematically outperform all other estimators under specific setups. By analyzing these cases, we identify fundamental estimation barriers and propose new tests that more effectively stress these specific limitations.  \nWe share the open source code at [https://github.com/VanessB/mutinfo](https://github.com/VanessB/mutinfo).  \n1 Introduction  \nMutual Information (mi) quantifies the statistical dependence between random variables and is fundamental to both theoretical frameworks and practical applications in machine learning, information theory, and statistical inference (Cover & Thomas, 2006; Polyanskiy & Wu, 2024) . Accurate estimation of mutual information is essential for a wide array of tasks, ranging from representation learning (Hjelm et al., 2019; van den Oord et al., 2019; Tschannen et al., 2020) and generative modeling (Chen et al., 2016; Wang et al., 2025a;b; Franzese et al., 2025) to feature selection (Sulaiman & Labadin, 2015; Huang et al., 2024) and hypothesis testing (Runge, 2018) . Despite significant progress, existing mi estimation methods exhibit substantial variance  \n∗ Equal contribution  \nin performance, interpretability, and scalability, highlighting the need for comprehensive and systematic benchmarking frameworks (Czyż et al., 2023) .  \nIn this work, we review and extend previous efforts to establish such frameworks by proposing an extensive benchmarking suite designed to rigorously evaluate classical, neural-based, and advanced continuous-time mi estimators across diverse scenarios. Our study encompasses both classical statistical distributions and novel, specifically engineered tasks intended to isolate the strengths and weaknesses of different estimator classes. We also disentangle estimator-specific limitations from some inherent problem challenges (e.g., numerical instability and intrinsic variance), thereby providing new insights into the fundament","cbCaidC4aXxyiRK0","https://ap.wps.com/l/cbCaidC4aXxyiRK0","pdf",991998,1,33,"English","en",105,"# Abstract\n# Introduction\n## Background and Motivation","[{\"question\":\"What limitation do existing mutual information (MI) benchmarks have according to the document?\",\"answer\":\"Existing benchmarks typically evaluate MI estimators on simplified, low-dimensional distributions, so their behavior on complex, realistic data remains largely unexplored.\"},{\"question\":\"How does the proposed benchmarking framework organize and generalize prior work?\",\"answer\":\"It is grounded in a unified copula-theoretic perspective that subsumes existing benchmarks as special cases.\"},{\"question\":\"Do the results show a single estimator that is always best?\",\"answer\":\"No. The document reports that there is no universal winner; each estimator category can outperform others under specific experimental setups.\"}]",1784182651,83,{"code":4,"msg":30,"data":31},"ok",{"site_id":24,"language":23,"slug":32,"title":13,"keywords":33,"description":14,"schema_data":34,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":27},"towards-diverse-and-comprehensive-benchmarks-for-mutual-information-estimation","",{"@graph":35,"@context":85},[36,53,68],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,47,50],{"item":40,"name":41,"@type":42,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":46},"https://docshare.wps.com/document/","Document",2,{"item":48,"name":12,"@type":42,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":42,"position":52},"https://docshare.wps.com/document/towards-diverse-and-comprehensive-benchmarks-for-mutual-information-estimation/82746/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":40,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-17","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 limitation do existing mutual information (MI) benchmarks have according to the document?","Question",{"text":75,"@type":76},"Existing benchmarks typically evaluate MI estimators on simplified, low-dimensional distributions, so their behavior on complex, realistic data remains largely unexplored.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does the proposed benchmarking framework organize and generalize prior work?",{"text":80,"@type":76},"It is grounded in a unified copula-theoretic perspective that subsumes existing benchmarks as special cases.",{"name":82,"@type":73,"acceptedAnswer":83},"Do the results show a single estimator that is always best?",{"text":84,"@type":76},"No. The document reports that there is no universal winner; 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