Primary Submission Category: Machine Learning and Causal Inference
Automatic Debiased Machine Learning for Smooth Functionals of Nonparametric M-Estimands
Authors: Lars van der Laan, Aurelien Bibaut, Nathan Kallus, Alex Luedkte, Lars van der Laan,
Presenting Author: Lars van der Laan*
We propose a unified framework for automatic debiased machine learning (autoDML) to perform inference on smooth functionals of infinite-dimensional M-estimands, defined as population risk minimizers over Hilbert spaces. By automating debiased estimation and inference procedures in causal inference and semiparametric statistics, our framework enables practitioners to construct valid estimators for complex parameters without requiring specialized expertise. The framework supports a generic models parameterized by Hilbert spaces, Neyman-orthogonal loss functions with unknown nuisance components, and nonlinear functionals of multiple M-estimands. We formalize the class of parameters efficiently estimable by autoDML as a novel class of nonparametric projection parameters, defined via orthogonal minimum loss objectives. We introduce three autoDML estimators based on one-step estimation, targeted minimum loss-based estimation, and the method of sieves. For data-driven model selection, we derive a novel decomposition of model approximation error for smooth functionals of M-estimands and propose adaptive debiased machine learning estimators that are superefficient and adaptive to the functional form of the M-estimand. Finally, we illustrate the flexibility of our framework by constructing autoDML estimators for the long-term survival under a beta-geometric model and the average treatment effect under a heterogeneous treatment effect model.