[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-202022-105":3,"detail-sidebar-cat-0-en-105":81,"doc-detail-202022-en":131},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":74,"head_meta":76,"extra_data":78,"updated_unix":80},105,"en","localized-debiased-machine-learning-efficient-inference-on-quantile-treatment-effects-and-beyond","Localized Debiased Machine Learning - Efficient Inference on Quantile Treatment Effects and Beyond","","This paper studies estimation of a low-dimensional target parameter defined implicitly through an estimating equation that contains high-dimensional nuisance functions depending on the target. A key setting is the efficient estimating equation for the (local) quantile treatment effect in causal inference, where conditional distribution quantities must be evaluated at the target quantile. Existing debiased machine learning requires learning nuisance models across all possible inputs, including the entire covariate-conditional distribution. The proposed localized debiased machine learning estimates nuisances only at a single rough initial guess, uses two regression tasks for (L)QTE, and achieves the same asymptotic behavior as an oracle with true nuisances under mild rate conditions.",{"@graph":14,"@context":73},[15,34,56],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/research-report/","Research & 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Linwood","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-10-31","2026-09-04",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",14,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"Why do existing debiased machine learning methods become burdensome for (L)QTE?","Question",{"text":63,"@type":64},"They require learning nuisance functions for all possible target-parameter inputs, which for (L)QTE means learning the full covariate-conditional cumulative distribution function (equivalently infinitely many binary regressions).","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"How does localized debiased machine learning (LDML) reduce the nuisance-learning burden?",{"text":68,"@type":64},"LDML estimates the target-dependent nuisance only at a single initial rough guess, avoiding estimation over the entire continuum or an ad-hoc discretized grid.",{"name":70,"@type":61,"acceptedAnswer":71},"What theoretical guarantee does LDML provide for efficient estimation?",{"text":72,"@type":64},"Under lax rate conditions, the estimator has the same favorable asymptotic behavior as an infeasible oracle estimator that uses the unknown true nuisances, and for (L)QTE the asymptotic variance matches the relevant semiparametric efficiency bound.","https://schema.org",{"og:url":32,"og:type":75,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":77,"canonical":32},"index,follow",{"doc_id":79,"site_id":7},202022,1788541129,{"code":4,"msg":82,"data":83},"success",[84,88,92,96,101,106,111,115,120,123,127],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":85,"show_sort_weight":86,"slug":87},"Story & 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\nNathan Kallus [kallus@cornell.edu](kallus@cornell.edu)  \nCornell Tech  \nCornell University  \n2 West Loop Rd, NY 10044, USA  \nXiaojie Mao [maoxj@sem.tsinghua.edu.cn](maoxj@sem.tsinghua.edu.cn)  \nSchool of Economics and Management Tsinghua University  \nBeijing, 100084, China  \nMasatoshi Uehara [mu223@cornell.edu](mu223@cornell.edu)  \nCornell Tech  \nCornell University  \n2 West Loop Rd, NY 10044, USA  \nEditor: David Sontag  \nAbstract  \nWe consider estimating a low-dimensional parameter in an estimating equation involving high-dimensional nuisance functions that depend on the target parameter as an input.  \nA central example is the e􀀎cient estimating equation for the (local) quantile treatment e􀀋ect ((L)QTE) in causal inference, which involves the covariate-conditional cumulative distribution function evaluated at the quantile to be estimated. Existing approaches based on 􀀍exibly estimating the nuisances and plugging in the estimates, such as debiased machine learning (DML), require we learn the nuisance at all possible inputs. For (L)QTE, DML requires we learn the whole covariate-conditional cumulative distribution function.  \nWe instead propose localized debiased machine learning (LDML), which avoids this burdensome step and needs only estimate nuisances at a single initial rough guess for the target parameter. For (L)QTE, LDML involves learning just two regression functions, a standard task for machine learning methods. We prove that under lax rate conditions our estimator has the same favorable asymptotic behavior as the infeasible estimator that uses the unknown true nuisances. Thus, LDML notably enables practically-feasible and theoretically-grounded e􀀎cient estimation of important quantities in causal inference such as (L)QTEs when we must control for many covariates and/or 􀀍exible relationships, as we demonstrate in empirical studies.  \nKeywords: Causal Inference, Neyman Orthogonality, Cross-􀀌tting, Instrumental Variables, Conditional Value at Risk, Expectiles  \n􀀍c2024 Kallus, Mao, Uehara.  \nLicense: CC-BY 4.0, see [https://creativecommons.org/licenses/by/4.0/](https://creativecommons.org/licenses/by/4.0/. Attribution)[. Attribution](https://creativecommons.org/licenses/by/4.0/. Attribution) requirements are provided  \nat [http://jmlr.org/papers/v25/23-0661.html](http://jmlr.org/papers/v25/23-0661.html).  \nKallus, Mao, Uehara  \n1. Introduction  \nIn this paper, we consider estimating parameters 􀀒 􀀃 = (􀀒; 􀀒) 2 􀀂 = 􀀂 1 􀀂 􀀂2 􀀒 Rd de􀀌ned as the (unique) solution to the following d-dimensional estimating equation:  \nP (Z; 􀀒; 􀀑 (Z; 􀀒1 ) ; 􀀑 (Z)) = 0; 􀀒 = (􀀒1 ; 􀀒2 ) 2 􀀂 1 􀀂 􀀂 2 ; (1)  \nwhere Z 2 Z are observed random variables, 􀀑 (Z; 􀀒1 ) and 􀀑(Z) are two unknown nuisance functions, and 0 is the zero vector in Rd. We hope to estimate 􀀒 􀀃 based on (Z1 ; : : : ; ZN ), N independent and identically distributed (iid) draws from the distribution P. As we will show, estimating equations of the form above are prevalent in e􀀎cient estimation in causal inference and missing data problems, with quantile treatment e􀀋ect (QTE) estimation (Section 1.1) as a prominent example, among many others (Section 1.2) .  \nOne important feature of Eq. (1) is that the nuisance 􀀑 (Z; 􀀒1 ) involves the parameters to be estimated as an input. This parameter-dependent nuisance raises several challengesand causes existing methods to be unstable and computationally burdensome. Speci􀀌cally, we could potentially use the observed data to estimate the nuisances 􀀑 (Z; 􀀒1 ) and 􀀑(Z) and then solve a sample analogue of Eq. (1) based on the estimated nuisances in order to estimate 􀀒􀀃 , possibly using cross-􀀌tting (Robins et al., 2008; Zheng and van der Laan, 2011; Chernozhukov et al., 2018a) . However, this requires estimating the nuisance 􀀑 (Z; 􀀒1 ) for all possible 􀀒 1 2 􀀂 1 , i.e. , learning in􀀌nitely many functions of Z, and then solving for the root of an estimated funct","cbCaiv7akZdsWJCf","https://ap.wps.com/l/cbCaiv7akZdsWJCf","pdf",656908,59,"English","# Abstract\n# 1. Introduction\n## 1.1 Quantile treatment effect\n## 1.2 Other estimating-equation examples\n# Keywords","[{\"question\":\"Why do existing debiased machine learning methods become burdensome for (L)QTE?\",\"answer\":\"They require learning nuisance functions for all possible target-parameter inputs, which for (L)QTE means learning the full covariate-conditional cumulative distribution function (equivalently infinitely many binary regressions).\"},{\"question\":\"How does localized debiased machine learning (LDML) reduce the nuisance-learning burden?\",\"answer\":\"LDML estimates the target-dependent nuisance only at a single initial rough guess, avoiding estimation over the entire continuum or an ad-hoc discretized grid.\"},{\"question\":\"What theoretical guarantee does LDML provide for efficient estimation?\",\"answer\":\"Under lax rate conditions, the estimator has the same favorable asymptotic behavior as an infeasible oracle estimator that uses the unknown true nuisances, and for (L)QTE the asymptotic variance matches the relevant semiparametric efficiency bound.\"}]","Localized Debiased Machine Learning - Efficient Inference on Quantile Treatment Effects and Beyond | PDF",149]