[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-124649-en":3,"doc-seo-124649-105":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},124649,549758146520,"Patrick","https://ap-avatar.wpscdn.com/avatar/80002397d8c0411e94?_k=1775819394049821470",8,"Research & Report","Average partial effect estimation using double machine learning - Abstract","Single-parameter summaries of variable effects aid interpretation, yet linear models can fail when they poorly match the conditional mean. This work targets the average partial effect, defined as the average slope of the regression function with respect to a chosen predictor, using a doubly robust semiparametric strategy. The method extends beyond fixed nuisance-function forms to arbitrary plug-in nuisance estimation, enabling modern machine learning estimators, including nondifferentiable regression.","Average partial effect estimation using double machine learning  \nHarvey Klyne University of Cambridge [h. klyne@statslab. cam. ac. uk](h. klyne@statslab. cam. ac. uk)  \nRajen D. Shah University of Cambridge [r. shah@statslab. cam. ac. uk](r. shah@statslab. cam. ac. uk)  \narXiv :2308 .09207v1 [math . ST] 17 Aug 2023  \nAugust 21, 2023  \nAbstract  \nSingle-parameter summaries of variable effects are desirable for ease of interpretation, but linear models, which would deliver these, may fit poorly to the data. A modern approach is to estimate the average partial effect—the average slope of the regression function with respect to the predictor of interest—using a doubly robust semiparametric procedure. Most existing work has focused on specific forms of nuisance function estimators. We extend the scope to arbitrary plug-in nuisance function estimation, allowing for the use of modern machine learning methods which in particular may deliver non-differentiable regression function estimates. Our procedure involves resmoothing a user-chosen first-stage regression estimator to produce a differentiable version, and modelling the conditional distribution of the predictors through a location–scale model. We show that our proposals lead to a semiparametric efficient estimator under relatively weak assumptions. Our theory makes use of a new result on the sub-Gaussianity of Lipschitz score functions that may be of independent interest. We demonstrate the attractive numerical performance of our approach in a variety of settings including ones with misspecification.  \n1 Introduction  \nA common goal of practical data analysis is to quantify the effect that a particular predictor or set of predictors X has on a response Y , whilst accounting for the contribution of a vector of other predictors Z. Single-parameter summaries are often desirable for ease-of-interpretability, as demonstrated by the popularity of (partially) linear models. Such models, however, may not adequately capture the conditional mean of the response, potentially invalidating conclusions drawn. Indeed the successes of model-agnostic regression methods such as XGBoost [Chen and Guestrin, 2016], random forests [Breiman, 2001] and deep learning [Goodfellow et al., 2016] in machine learning competitions such as those hosted by Kaggle [Bojer and Meldgaard, 2021] suggest that such models fitting poorly is to be expected in many contemporary datasets of interest.  \nWhen X ∈ R is a continuous random variable and the conditional mean f(x, z) := E(Y | X = x, Z = z) is differentiable in the x-direction, a natural quantity of interest is the average slope with respect to x, holding Z constant. This is known as the average partial effect (or average derivative), defined as  \nθ := E 􀀔 f (X, Z)􀀕 .  \nThis has historically been considered for estimation of linear coefficients in index models [Stoker, 1986, Powell et al., 1989], but may be thought of more generally as the average effect of incrementing the value of X by an infinitesimal amount, holding Z constant. It is also the average  \nslope of the so-called partial dependence plot, popular in the field of interpretable machine learning [Friedman, 2001, Zhao and Hastie, 2021, Molnar, 2022] .  \nRothenh¨ausler and Yu [2020] provide a causal interpretation of this quantity in the form of an average outcome change if the ‘treatment’X of all subjects were changed by an arbitrarily small quantity. In this sense, θ may be thought of as a continuous analogue of the well-studied average treatment effect functional E{E(Y | Z, X = 1) − E(Y | Z, X = 0)} = E{f(1, Z) − f(0, Z)} in the case where X is discrete, only taking values 0 or 1 [Robins et al. , 1994, Robins and Rotnitzky, 1995, Scharfstein et al., 1999a] .  \nNote also that in the partially linear model  \nf (x, z) = θx + g(z),  \nthe average partial effect reduces to the linear coefficient. Thus the average partial effect maybe thought of as a generalisation of the coefficient in a partially linear mo","cbCaiaJhbNKfHWUT","https://ap.wps.com/l/cbCaiaJhbNKfHWUT","pdf",1617684,1,61,"English","en",105,"# Abstract\n## Introduction","[{\"question\":\"What is the average partial effect in this document?\",\"answer\":\"It is the expected slope of the conditional regression function with respect to a predictor of interest, averaging over the joint distribution while holding other variables fixed.\"},{\"question\":\"Why is estimating the average partial effect difficult?\",\"answer\":\" Derivative estimates from flexible regression methods can be unstable or unusable, and plug-in bias can prevent the estimator from achieving fast, parametric convergence, complicating inference.\"},{\"question\":\"How does the proposed approach handle nuisance functions and machine learning models?\",\"answer\":\"It uses a doubly robust semiparametric procedure that allows arbitrary plug-in nuisance function estimation, including machine learning methods that may yield nondifferentiable regression estimates.\"}]","Average partial effect estimation using double machine learning - Abstract | PDF",1785893520,154,{"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},"average-partial-effect-estimation-using-double-machine-learning-abstract","",{"@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/average-partial-effect-estimation-using-double-machine-learning-abstract/124649/",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 is the average partial effect in this document?","Question",{"text":75,"@type":76},"It is the expected slope of the conditional regression function with respect to a predictor of interest, averaging over the joint distribution while holding other variables fixed.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"Why is estimating the average partial effect difficult?",{"text":80,"@type":76},"Derivative estimates from flexible regression methods can be unstable or unusable, and plug-in bias can prevent the estimator from achieving fast, parametric convergence, complicating inference.",{"name":82,"@type":73,"acceptedAnswer":83},"How does the proposed approach handle nuisance functions and machine learning models?",{"text":84,"@type":76},"It uses a doubly robust semiparametric procedure that allows arbitrary plug-in nuisance function estimation, including machine learning methods that may yield nondifferentiable regression 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},[93,97,101,105,110,115,120,123,128,131,135],{"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":121,"slug":122},30,"research-report",{"id":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":132,"doc_module":4,"doc_module_name":46,"category_name":133,"show_sort_weight":132,"slug":134},10,"Lifestyle","lifestyle",{"id":136,"doc_module":4,"doc_module_name":46,"category_name":137,"show_sort_weight":106,"slug":138},19,"General","general"]