[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-124578-en":3,"doc-seo-124578-105":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":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":27,"seo_description":14,"update_tm":28,"read_time":29},124578,1099513958762,"Logic","https://ap-avatar.wpscdn.com/avatar/1000023916a998db790?x-image-process=image/resize,m_fixed,w_180,h_180&k=1784791008015729253",8,"Research & Report","Shapley Values with Uncertain Value Functions","A probability-theoretic, first-principles framework is used to define Shapley values under uncertain value functions, motivated by non-deterministic algorithms encountered in explainable machine learning. The work shows that randomness in the evaluation can be incorporated into a Shapley formulation by moving it into a noiseless but shifted value function. As a result, uncertain-value Shapley values can be treated analogously to standard Shapley values, while reliable estimation typically demands increased computational effort.","arXiv :2301 .08086v1 [ cs .LG] 19 Jan 2023  \nShapley Values with Uncertain Value Functions  \nRaoul Heese 1 , Sascha M􀁿ucke2 , Matthias Jakobs2 , Thore Gerlach3 , and Nico Piatkowski3  \n1 Fraunhofer [ITWM](ITWM raoul.heese@itwm.fraunhofer.de)[ raoul.heese@itwm.fraunhofer.de](ITWM raoul.heese@itwm.fraunhofer.de)  \n2 TU Dortmund  \n3 Fraunhofer IAIS  \nAbstract. We propose a novel de􀀌nition of Shapley values with uncertain value functions based on 􀀌rst principles using probability theory. Such uncertain value functions can arise in the context of explainable machine learning as a result of non-deterministic algorithms. We show that random e􀀋ects can in fact be absorbed into a Shapley value with a noiseless but shifted value function. Hence, Shapley values with uncertain value functions can be used in analogy to regular Shapley values. However, their reliable evaluation typically requires more computational e􀀋ort.  \nKeywords: Shapley Values · Uncertainty · Explainable Machine Learning · Game Theory  \n1 Introduction  \nThe ability to interpret the predictions of machine learning (ML) models is an important requirement for many data-driven decision support applications, e. g. , in computational biology [1], medicine [2], materials science [3], and 􀀌nance [4], just to name a few. There are a variety of model-agnostic methods that enable explainability of otherwise black-box models [5] . The theory of Shapley values (SVs) [6], a concept from coalitional game theory, builds the foundation for a collection of such methods [7,8,9,10,11,12] . They all have in common that a SV|in the sense of an importance score|is attributed to each feature of an arbitrary predictive model. Based on these scores, explanations can be made about which features are responsible for which prediction. For a recent review of SVs in explainable ML (XML), see, e. g., [13,14] and references therein.  \nSVs for XML are based on the premise of a value function (VF) that quanti􀀌es the impact of each feature to a model's prediction by a real number. There are various approaches to de􀀌ne suitable VFs for such a task [12], but their evaluation typically involves a statistical or randomized (i. e., non-deterministic) ingredient. For example, a straightforward approach for a classi􀀌er is toretrain the model for all possible feature combinations and use its prediction of class probabilities to specify the VF [15] . However, the training procedure os often a randomized algorithm, e. g. , due to random initializations, data splitting, or randomized search heuristics|leading to di􀀋erent outcomes if repeated with di􀀋erent random seeds. As a result, the corresponding VF becomes a random variable that yields di􀀋erent outcomes if evaluated multiple times.  \nThe e􀀋ect of uncertain VFs for SVs in the context of XML has not been extensively studied in the literature before. To our knowledge, [16], which is based on the DeepSHAP approximation [17,10], is the only work in this direction. Therein, a purely empirical perspective on sampling uncertainty is studied without any explicit sources of randomness. More generally, in [18,19], the authors de􀀌ne the uncertainty of coalition games as the standard deviation when considering the marginal contributions of each player entering a random coalition, which can also be understood  \n2 R. Heese et al.  \nas a measure of the strategic risk. An important insight is that whenever two players have the same SVs, they do not necessarily share the same risk. However, no randomness from the VF is considered in these works. In [20,21], the authors study uncertain coalition games [22] based on uncertainty theory [23] and introduce risk averse SVs. A brief review of related work can also be found in [21] . Since the calculus of uncertainty theory is based on special assumptions, the results are not straightforwardly applicable to the uncertainties that arise for SVs in the context of XML. In conclusion, there is no self-consistent work on SVs with uncertain V","cbCaiuRgTAuhtlm0","https://ap.wps.com/l/cbCaiuRgTAuhtlm0","pdf",549840,1,12,"English","en",105,"# Introduction\n## Related Background on Shapley Values\n## Uncertain Value Functions in Explainable ML\n# Shapley Values\n## Core Game-Theoretic Premise","[{\"question\":\"What problem does the paper address regarding Shapley values in explainable machine learning?\",\"answer\":\"It addresses how Shapley values behave when the underlying value function is uncertain due to non-deterministic elements in model evaluation. This uncertainty can cause variability when explanations are recomputed.\"},{\"question\":\"How are uncertain value functions incorporated into the proposed Shapley formulation?\",\"answer\":\"Random effects are absorbed into a Shapley value using a noiseless but shifted value function. The shift is determined by the mean bias of marginal contributions.\"},{\"question\":\"What trade-off is noted for evaluating Shapley values with uncertain value functions?\",\"answer\":\"Reliable evaluation typically requires more computational effort, depending on the desired confidence level for the estimates.\"}]","Shapley Values with Uncertain Value Functions | PDF",1785893102,30,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"shapley-values-with-uncertain-value-functions","",{"@graph":36,"@context":85},[37,54,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"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":53},"https://docshare.wps.com/document/shapley-values-with-uncertain-value-functions/124578/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":62,"encodingFormat":61,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-05",true,{"@type":65,"interactionType":66,"userInteractionCount":4},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What problem does the paper address regarding Shapley values in explainable machine learning?","Question",{"text":75,"@type":76},"It addresses how Shapley values behave when the underlying value function is uncertain due to non-deterministic elements in model evaluation. This uncertainty can cause variability when explanations are recomputed.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How are uncertain value functions incorporated into the proposed Shapley formulation?",{"text":80,"@type":76},"Random effects are absorbed into a Shapley value using a noiseless but shifted value function. The shift is determined by the mean bias of marginal contributions.",{"name":82,"@type":73,"acceptedAnswer":83},"What trade-off is noted for evaluating Shapley values with uncertain value functions?",{"text":84,"@type":76},"Reliable evaluation typically requires more computational effort, depending on the desired confidence level for the estimates.","https://schema.org",{"og:url":52,"og:type":87,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":89,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,122,127,130,134],{"id":20,"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":53,"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":29,"slug":121},"research-report",{"id":123,"doc_module":4,"doc_module_name":46,"category_name":124,"show_sort_weight":125,"slug":126},9,"Religion & Spirituality",20,"religion-spirituality",{"id":125,"doc_module":4,"doc_module_name":46,"category_name":128,"show_sort_weight":125,"slug":129},"World Cup","world-cup",{"id":131,"doc_module":4,"doc_module_name":46,"category_name":132,"show_sort_weight":131,"slug":133},10,"Lifestyle","lifestyle",{"id":135,"doc_module":4,"doc_module_name":46,"category_name":136,"show_sort_weight":106,"slug":137},19,"General","general"]