Localized Debiased Machine Learning: Efficient Inference on Quantile Treatment Effects and Beyond

2019/12/30 by Nathan Kallus, Kallus, Nathan, Xiaojie Mao +3 · 7 citations
Mathematics · #Advanced Causal Inference Techniques #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Methodology (stat.ME) #Statistical Methods and Bayesian Inference #Statistical Methods and Inference

paper · pdf · doi:10.48550/arxiv.1912.12945

openalex publication_date 2019/12/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider estimating a low-dimensional parameter in an estimating equation involving high-dimensional nuisances that depend on the parameter. A central example is the efficient estimating equation for the (local) quantile treatment effect ((L)QTE) in causal inference, which involves as a nuisance the covariate-conditional cumulative distribution function evaluated at the quantile to be estimated. Debiased machine learning (DML) is a data-splitting approach to estimating high-dimensional nuisances using flexible machine learning methods, but applying it to problems with parameter-dependent nuisances is impractical. For (L)QTE, DML requires we learn the whole covariate-conditional cumulative distribution function. We 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 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 efficient estimation of important quantities in causal inference such as (L)QTEs when we must control for many covariates and/or flexible relationships, as we demonstrate in empirical studies.

Citations

• High-Dimensional Methods and Inference on Structural and Treatment Effects
• Orthogonal Random Forest for Causal Inference
• A general theory of hypothesis tests and confidence regions for sparse high dimensional models
• Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score

Cited by

• Towards an Asymptotic Efficiency Theory on Regular Parameter Manifolds
• Federated Learning of Quantile Inference under Local Differential Privacy
• Beyond the Average: Distributional Causal Inference under Imperfect Compliance
• Inference on Nonlinear Counterfactual Functionals under a Multiplicative IV Model
• Median Optimal Treatment Regimes
• Efficient and Scalable Estimation of Distributional Treatment Effects with Multi-Task Neural Networks
• A New and Efficient Debiased Estimation of General Treatment Models by Balanced Neural Networks Weighting

Related

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• Debiased Machine Learning when Nuisance Parameters Appear in Indicator Functions
• A Simple and General Debiased Machine Learning Theorem with Finite\n Sample Guarantees
• Doubly Robust Estimation of Direct and Indirect Quantile Treatment Effects with Machine Learning