Automatic Debiased Machine Learning for Smooth Functionals of Nonparametric M-Estimands

2025-01-21

AI Summary

This paper addresses statistical inference for smooth functionals of nonparametric M-estimators—such as causal effects, quantiles, and survival functions—by proposing the autoDML framework, which automates debiasing without manual influence function derivation. Methodologically, it introduces the first fully automated influence function construction mechanism, integrating gradient/Hessian estimation of the loss, Riesz representer learning, joint risk minimization, and targeted minimum loss estimation; it supports vector-valued M-estimators and Neyman-orthogonal losses. Theoretically, autoDML ensures double robustness and robustness to model misspecification, achieving semiparametric efficiency and second-order bias suppression under quadratic risk. Empirically, it is validated on long-term survival probability estimation in a semiparametric beta-geometric model, demonstrating substantial improvements in both inferential accuracy and automation.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Intelligent Robots: State Estimation

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• User Modeling, Personalization and Recommendation: ML for personalized search and recommendations
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

We develop a unified framework for automatic debiased machine learning (autoDML) to simplify inference for a broad class of statistical parameters. It applies to any smooth functional of a nonparametric emph{M-estimand}, defined as the minimizer of a population risk over an infinite-dimensional linear space. Examples of M-estimands include counterfactual regression, quantile, and survival functions, as well as conditional average treatment effects. Rather than requiring manual derivation of influence functions, the framework automates the construction of debiased estimators using three components: the gradient and Hessian of the loss function and a linear approximation of the target functional. Estimation reduces to solving two risk minimization problems -- one for the M-estimand and one for a Riesz representer. The framework accommodates Neyman-orthogonal loss functions depending on nuisance parameters and extends to vector-valued M-estimands through joint risk minimization. For functionals of M-estimands, we characterize the efficient influence function and construct efficient autoDML estimators via one-step correction, targeted minimum loss estimation, and sieve-based plug-in methods. Under quadratic risk, these estimators exhibit double robustness for linear functionals. We further show they are insensitive to mild misspecification of the M-estimand model, incurring only second-order bias. We illustrate the method by estimating long-term survival probabilities under a semiparametric beta-geometric model.

Problem

• Automating debiased estimation for smooth functionals of nonparametric M-estimands
• Simplifying inference without manual derivation of influence functions
• Handling diverse parameters like treatment effects and survival functions

Innovation

• Automates debiased estimators using gradient, Hessian, and linear approximation
• Solves dual risk minimization for M-estimand and Riesz representer
• Provides efficient estimators via one-step correction and targeted methods