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

TL;DR

This paper introduces an automated framework for debiased machine learning that simplifies inference on complex statistical parameters by avoiding manual influence function derivation, applicable to various smooth functionals of nonparametric estimands.

Contribution

The authors develop autoDML, a unified, automated approach for constructing debiased estimators for a broad class of functionals, extending to vector-valued cases and offering robustness to model misspecification.

Findings

Framework automates influence function construction

Estimators achieve double robustness and second-order bias correction

Successfully applied to survival probability estimation

Abstract

We develop a unified framework for automatic debiased machine learning (autoDML) for inference on a broad class of statistical parameters. The framework applies to any smooth functional of a nonparametric M-estimand, defined as the minimizer of a population risk over an infinite-dimensional linear space. Examples include counterfactual regression, quantile, and survival functions, as well as conditional average treatment effects. Rather than requiring manual derivation of influence functions, our approach automates the construction of debiased estimators using three ingredients: 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 that depend on nuisance parameters and extends to vector-valued M-estimands through joint risk minimization. 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 satisfy double robustness for linear functionals. We further show that they are robust 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 two-parameter beta-geometric failure model.