[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-82739-en":3,"doc-seo-82739-105":29,"detail-sidebar-cat-0-en-105":90},{"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":4,"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},82739,4398048949847,"Eliana","https://ap-avatar.wpscdn.com/avatar/400002536579ef2da7f?_k=1778318612642679267",8,"Research & Report","Asymptotic Analysis of the Shapley Value for Dataset Valuation","An asymptotic analysis addresses Shapley-value-based dataset valuation where utilities are expressed as smooth functionals of empirical distributions using RKHS mean embeddings. The work shows that, although Shapley value is defined through a combinatorial averaging over coalitions, it is asymptotically governed by a simple leading term. This term reflects the first-order contribution of a dataset relative to the surrounding population, revealing Shapley scaling with the number of dataset sources. It also supports benchmarking and analysis of Shapley estimators.","An Asymptotic Analysis of the Shapley Value for  \nDataset Valuation  \nMélissa Tamine ∗  \nCriteo AI lab, FairPlay joint team, France CREST, ENSAE, Institut Polytechnique de Paris [m.tamine@criteo.com](m.tamine@criteo.com)  \nBenjamin Heymann  \nCriteo AI lab, FairPlay joint team, France [b.heymann@criteo.com](b.heymann@criteo.com)  \narXiv :2607 .03374v 1 [ cs .GT] 3 Jul 2026  \nMaxime Vono  \nCriteo AI lab, FairPlay joint team, France [m.vono@criteo.com](m.vono@criteo.com)  \nPatrick Loiseau  \nInria, FairPlay joint team, France [patrick.loiseau@inria.fr](patrick.loiseau@inria.fr)  \nAbstract  \nWe propose an asymptotic analysis of the Shapley value in a dataset valuation setting in which utilities are modeled as smooth functionals of empirical distributions via reproducing kernel Hilbert space (RKHS) mean embeddings. We prove that, despite its combinatorial definition, the Shapley value of a data source is asymptotically captured by a simple leading term. This term can be interpreted asthe first-order contribution of a dataset relative to the surrounding data population.  \nIt also identifies the scale of the Shapley value as the number of data sources grows and provides a framework for analyzing existing Shapley value estimators.  \nMoreover, for practitioners working with large numbers of datasets, the leading term becomes a tractable reference against which Shapley value approximationscan be benchmarked.  \n1 Introduction  \nAchieving strong generalization in machine learning often requires more data than any single party can access on its own. In many applications, the relevant data are naturally distributed across several contributors, each holding only a partial and potentially complementary view of the learning problem at hand. In online advertising, for instance, different retailers may hold complementary information about users’ browsing and purchasing behavior. Taken separately, these datasets provide only a partial picture, but taken together, they may support significantly better models. Such collaborative settings raise a natural question: if several contributors jointly enable the success of a learning task, how should that value be attributed back to their respective datasets? This is the dataset valuation problem [1, 35, 31] . It generalizes the more popular data valuation problem [30, 14], with data valuation being the special case of dataset valuation in which each owner contributes exactly one data point. A natural way to formalize it is through cooperative game theory: each dataset owner is modeled as a player, each coalition of players is assigned a utility reflecting the performance achieved by pooling their data, and a valuation rule is then used to distribute this utility among contributors [9, 12] . Among the solution concepts considered for this purpose, the Shapley value [29] has become the most prominent in machine learning because it enjoys a strong axiomatic justification.  \nA major challenge in using the Shapley value is its computational intractability. For a fixed game with I players, the Shapley value of one player averages its marginal contribution over all subsets of the other I − 1 players. Computing it exactly, therefore, requires evaluating exponentially  \n∗Corresponding author.  \nPreprint.  \nmany coalitions. This has motivated a substantial literature on scalable approximations in the context of dataset valuation [21, 37, 3, 5, 38, 32, 34], including permutation-based Monte Carlo methods [22, 9, 12], group-testing-based accelerations [12], and dataset-level proxies such as DU-Shapley [7] . These works address the problem of Shapley estimation for a fixed number of players.  \nOur paper is orthogonal to this fixed-game perspective and, to our knowledge, provides the first asymptotic analysis of the Shapley value in a dataset valuation setting. The main result is a finite-I bound which, interpreted asymptotically, shows that the Shapley value is close to a simple leading term. This leading term depends","cbCaigpY1L0qqANb","https://ap.wps.com/l/cbCaigpY1L0qqANb","pdf",823266,1,37,"English","en",105,"# Abstract\n# Introduction\n## Dataset valuation and Shapley value\n## Computational intractability and existing estimators\n## Fixed-game vs asymptotic viewpoint\n## Smooth utilities via RKHS mean embeddings\n# Main contributions","[{\"question\":\"What mathematical framework is used to model utilities for dataset valuation?\",\"answer\":\"Utilities are modeled as smooth functionals of empirical distributions via reproducing kernel Hilbert space (RKHS) mean embeddings. This representation enables perturbation and first-order analysis for large coalitions.\"},{\"question\":\"Why is Shapley value difficult to compute, and what do prior works focus on?\",\"answer\":\"Computing Shapley value exactly requires averaging marginal contributions across all subsets of other players, which grows exponentially with the number of players. Prior work develops scalable approximation methods, including permutation-based Monte Carlo, group-testing accelerations, and dataset-level proxies.\"},{\"question\":\"How does the paper define the asymptotic regime when the Shapley value is defined for fixed finite players?\",\"answer\":\"It fixes a single data owner i and keeps its dataset Di unchanged, then forms larger games by adding surrounding data owners sampled independently from a common population. The paper studies the sequence of Shapley values ϕ_i^I as I grows.\"}]",1784182600,93,{"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":85,"head_meta":87,"extra_data":89,"updated_unix":27},"asymptotic-analysis-of-the-shapley-value-for-dataset-valuation","",{"@graph":35,"@context":84},[36,53,67],{"@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/asymptotic-analysis-of-the-shapley-value-for-dataset-valuation/82739/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":61,"encodingFormat":60,"isAccessibleForFree":62,"interactionStatistic":63},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":40,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-16",true,{"@type":64,"interactionType":65,"userInteractionCount":4},"InteractionCounter",{"@type":66},"ViewAction",{"@type":68,"mainEntity":69},"FAQPage",[70,76,80],{"name":71,"@type":72,"acceptedAnswer":73},"What mathematical framework is used to model utilities for dataset valuation?","Question",{"text":74,"@type":75},"Utilities are modeled as smooth functionals of empirical distributions via reproducing kernel Hilbert space (RKHS) mean embeddings. This representation enables perturbation and first-order analysis for large coalitions.","Answer",{"name":77,"@type":72,"acceptedAnswer":78},"Why is Shapley value difficult to compute, and what do prior works focus on?",{"text":79,"@type":75},"Computing Shapley value exactly requires averaging marginal contributions across all subsets of other players, which grows exponentially with the number of players. Prior work develops scalable approximation methods, including permutation-based Monte Carlo, group-testing accelerations, and dataset-level proxies.",{"name":81,"@type":72,"acceptedAnswer":82},"How does the paper define the asymptotic regime when the Shapley value is defined for fixed finite players?",{"text":83,"@type":75},"It fixes a single data owner i and keeps its dataset Di unchanged, then forms larger games by adding surrounding data owners sampled independently from a common population. 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