[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-118745-en":3,"doc-seo-118745-105":30,"detail-sidebar-cat-0-en-105":92},{"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":27,"seo_description":14,"update_tm":28,"read_time":29},118745,1099513958762,"Logic","https://ap-avatar.wpscdn.com/avatar/1000023916a998db790?x-image-process=image/resize,m_fixed,w_180,h_180&k=1784791008015729253",8,"Research & Report","Derivative-based Shapley value for global sensitivity analysis and machine learning explainability","Introduces a derivative-based Shapley value framework for global sensitivity analysis and machine learning explainability. The approach computes feature contributions using first-order partial derivatives of the underlying model function. Its computational complexity scales linearly with the number of features, avoiding the exponential cost common in other Shapley-value methods. Numerical experiments across global sensitivity analysis and explainability tasks benchmark DerSHAP against activity scores, SHAP, and KernelSHAP.","arXiv :2303 . 15183v1 [ cs .LG] 24 Mar 2023  \nDERIVATIVE-BASED SHAPLEY VALUE FOR GLOBAL SENSITIVITY ANALYSIS AND MACHINE LEARNING EXPLAINABILITY  \nHUI DUAN􀀃 AND GIRAY KTENy  \nAbstract. We introduce a new Shapley value approach for global sensitivity analysis and machine learning explainability. The method is based on the 􀀌rst-order partial derivatives of the underlying function. The computational complexity of the method is linear in dimension (number of features), as opposed to the exponential complexity of other Shapley value approaches in the literature. Examples from global sensitivity analysis and machine learning are used to compare the method numerically with activity scores, SHAP, and KernelSHAP.  \nKey words. Shapley value; activity scores; derivative-based global sensitivity measures; Sobol'sensitivity indices; global sensitivity analysis; machine learning explainability  \n1. Introduction. Global sensitivity analysis is the study of how uncertainty in the output of a model can be allocated to uncertainties in the model input. The applications of sensitivity analysis cover a wide range of disciplines, from natural sciences to engineering, and social sciences to mathematical sciences. Several methods for global sensitivity analysis have been introduced in the literature, including Sobol' sensitivity indices, derivative-based global sensitivity measures (DGSM), activity scores, and Shapley values. In this paper, we introduce a derivative-based Shapley value (DerSHAP) approach for global sensitivity analysis and machine learning explainability.  \nThe paper is organized as follows. In Section 2 we discuss Sobol' sensitivity indices, derivative-based global sensitivity measures, and activity scores. In Section 3 we review the Shapley value, and in Section 4 we introduce our method, the derivativebased Shapley value (DerSHAP) . In Section 5 we use DerSHAP to perform global sensitivity analysis of an Ebola model and an HIV model, and compare it numerically with the activity score approach. We also apply DerSHAP to two datasets from machine learning, Amazon stock data and Boston housing data, and compare it with SHAP and KernelSHAP. Conclusions follow in the last section.  \n2. Global Sensitivity Analysis. In this section, we review some of the background material from global sensitivity analysis. We will give a review of Sobol'sensitivity indices, derivative based global sensitivity measures (DGSM), and activity scores.  \n2.1. Sobol' Sensitivity Indices. Consider a d dimensional input vector x =(x1 ; : : : ; xd ) with the index set D = f1; 2; : : : ; dg. Let f (x) be a square-integrable function de􀀌ned on (0 ; 1)d. The ANOVA decomposition of f (x) is expressed as  \nf (x) = X fu (xu );  \nu􀀒D  \nwhere fu (xu ) is the component function that only depends on xu. For the empty set, we have f; = R f (x)dx.  \nIf we assume x has uniform distribution on (0 ; 1)d , we can write  \nE [f(x)] = Z(0 ; 1)d f (x)dx;  \n􀀃 Department of Mathematics, Florida State University, Tallahassee FL, USA (hd[uan@math.fsu.edu](uan@math.fsu.edu)).  \ny Department of Mathematics, Florida State University, Tallahassee FL, USA ([okten@fsu.edu](okten@fsu.edu)) .  \n1  \nThis manuscript is for review purposes only.  \n2 HUI DUAN AND GIRAY KTEN  \nand  \nVar(f(x)) = 􀀛2 = Z(0 ; 1)d f 2 (x)dx 􀀀 E[f(x)]2 : Due to the orthogonality of the ANOVA decomposition, the variance of f can be  \nwritten as  \n􀀛 2 = X 􀀛2u ;  \nu􀀒D  \nwhere 􀀛2u is the variance for the component function fu:  \n2  \n􀀛2u = Z(0 ; 1)d f2u(x)dx 􀀀Z(0 ; 1)d fu (x)dx! = Z(0 ; 1)d f2u(x)dx:  \nThe Sobol' sensitivity indices for the subset u are de􀀌ned from the variances of component functions  \nSu = 􀀛12 vX􀀒u 􀀛2v = ~~􀀜~~􀀛~~u~~2 and Su = 􀀛12 v XT u; 􀀛2v = 􀀜􀀛u2 ;  \nwhere Su is called the lower Sobol' sensitivity index (or, the main e􀀋ect) and Su is called the upper Sobol' sensitivity index (or, the total e􀀋ect) . If Su is close to 1, then the parameters xu are viewed as very important to the model. In practical applicati","cbCaipK6usYJfBd5","https://ap.wps.com/l/cbCaipK6usYJfBd5","pdf",1185058,1,15,"English","en",105,"# Introduction\n## Global sensitivity analysis background\n# Derivative-based Shapley value (DerSHAP)\n## Comparison with sensitivity and explainability methods\n## Applications: Ebola, HIV, Amazon stock, Boston housing","[{\"question\":\"What does the derivative-based Shapley value method aim to explain?\",\"answer\":\"It allocates feature-level contributions for both global sensitivity analysis and machine learning explainability by using first-order partial derivatives.\"},{\"question\":\"How does DerSHAP's computational complexity scale with the number of features?\",\"answer\":\"The method has linear complexity in the dimension (the number of features), unlike exponential complexity in other Shapley-value approaches.\"},{\"question\":\"Which methods does DerSHAP get compared against in the paper?\",\"answer\":\"The paper compares DerSHAP numerically with activity scores, SHAP, and KernelSHAP, and also considers Sobol’ sensitivity indices and related derivative-based sensitivity measures as background.\"}]","Derivative-based Shapley value for global sensitivity analysis and machine learning explainability | PDF",1785720029,38,{"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":87,"head_meta":89,"extra_data":91,"updated_unix":28},"derivative-based-shapley-value-for-global-sensitivity-analysis-and-machine-learning-explainability","",{"@graph":36,"@context":86},[37,54,69],{"@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/derivative-based-shapley-value-for-global-sensitivity-analysis-and-machine-learning-explainability/118745/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":63,"encodingFormat":61,"isAccessibleForFree":64,"interactionStatistic":65},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-04","2026-08-03",true,{"@type":66,"interactionType":67,"userInteractionCount":20},"InteractionCounter",{"@type":68},"ViewAction",{"@type":70,"mainEntity":71},"FAQPage",[72,78,82],{"name":73,"@type":74,"acceptedAnswer":75},"What does the derivative-based Shapley value method aim to explain?","Question",{"text":76,"@type":77},"It allocates feature-level contributions for both global sensitivity analysis and machine learning explainability by using first-order partial derivatives.","Answer",{"name":79,"@type":74,"acceptedAnswer":80},"How does DerSHAP's computational complexity scale with the number of features?",{"text":81,"@type":77},"The method has linear complexity in the dimension (the number of features), unlike exponential complexity in other Shapley-value approaches.",{"name":83,"@type":74,"acceptedAnswer":84},"Which methods does DerSHAP get compared against in the paper?",{"text":85,"@type":77},"The paper compares DerSHAP numerically with activity scores, SHAP, and KernelSHAP, and also considers Sobol’ sensitivity indices and related derivative-based sensitivity measures as background.","https://schema.org",{"og:url":52,"og:type":88,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":90,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":93},[94,98,102,106,111,116,121,124,129,132,136],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":95,"show_sort_weight":96,"slug":97},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":99,"show_sort_weight":100,"slug":101},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":103,"show_sort_weight":104,"slug":105},"Exam",70,"exam",{"id":107,"doc_module":4,"doc_module_name":46,"category_name":108,"show_sort_weight":109,"slug":110},5,"Comic",60,"comic",{"id":112,"doc_module":4,"doc_module_name":46,"category_name":113,"show_sort_weight":114,"slug":115},6,"Technology",50,"technology",{"id":117,"doc_module":4,"doc_module_name":46,"category_name":118,"show_sort_weight":119,"slug":120},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":122,"slug":123},30,"research-report",{"id":125,"doc_module":4,"doc_module_name":46,"category_name":126,"show_sort_weight":127,"slug":128},9,"Religion & Spirituality",20,"religion-spirituality",{"id":127,"doc_module":4,"doc_module_name":46,"category_name":130,"show_sort_weight":127,"slug":131},"World Cup","world-cup",{"id":133,"doc_module":4,"doc_module_name":46,"category_name":134,"show_sort_weight":133,"slug":135},10,"Lifestyle","lifestyle",{"id":137,"doc_module":4,"doc_module_name":46,"category_name":138,"show_sort_weight":107,"slug":139},19,"General","general"]