Improved Debiased Machine Learning through Optimization and Calibration

Abstract

Debiased machine learning uses flexible, data-adaptive methods to estimatecausal and statistical targets while correcting bias from nuisance estimation. This dissertation develops calibration- and optimization-based approaches for debiased inference and learning. The first part develops calibrated debiased machine learning for inference on linear summaries of regression functions. Standard doubly robust estimators are consistent if either the regression function or its Riesz representer is consistently estimated, but asymptotic normality typically requires both nuisances to converge sufficiently quickly. We show that calibrating nuisance estimators in AIPW procedures yields doubly robust asymptotic linearity: under partial-orthogonality conditions, these estimators are asymptotically normal when either nuisance component is estimated well, while the other may converge slowly or inconsistently. The second part introduces efficient plug-in learning for heterogeneous causal effect estimation. It constructs debiased, efficient plug-in estimators of population risks for causal contrasts, including conditional average treatment effects and relative risks, using a TMLE-style sieve correction. These estimators retain the oracle-efficiency properties of orthogonal statistical learning while avoiding unstable pseudo-outcomes and nonconvex losses. The third part develops automatic debiased machine learning for smooth functionals of nonparametric M-estimands. This extends automatic debiasing beyond regression functions to infinite-dimensional population risk minimizers. The central object is the Hessian Riesz representer of the target derivative, which determines the leading plug-in bias and influence-function correction, reducing automatic debiasing to two risk minimization problems: one for the M-estimand and one for the representer.