Debiased Machine Learning: Identification, Estimation, and Shape Constraints

2026-07-27

AI Summary

This study addresses the regularization bias and overfitting commonly induced by high-dimensional nuisance parameters in target parameter estimation. The authors propose a general debiased machine learning framework that identifies the target parameter through moment conditions and corrects the bias introduced by machine learning estimates of high-dimensional nuisance components via the Riesz representer. They innovatively show that the Riesz representer is uniquely determined by a quadratic functional and incorporate shape constraints into the nonlinear parameter space to mitigate the curse of dimensionality and enhance estimation accuracy. The method combines sieve techniques with deep neural networks to estimate nuisance functions while jointly integrating shape constraints and Riesz representer estimation. Simulation and empirical results demonstrate that the proposed framework achieves unbiased and more precise parameter estimates in high-dimensional settings.

Abstract

We develop a general framework of identification and estimation for automatic debiased machine learning (DML) where the parameter of interest $θ_0$ is identified by a moment condition involving a nuisance $γ_0$ that may be high dimensional. DML leverages machine learning to estimate $γ_0$ while correcting for regularization and overfitting biases that may otherwise transmit to biased estimation of $θ_0$. We establish conditions under which the Riesz representer $α_0$, which is at the core of DML, is identified, and show that the identification occurs precisely when $α_0$ uniquely optimizes a quadratic functional. This characterization enables us to develop a general estimation procedure for $α_0$ that allows for generic $γ_0$ including those defined by models with endogeneity and encompasses both classical sieves and modern architectures such as deep neural networks. To improve estimation precision and mitigate the curse of dimensionality, we incorporate shape constraints on $γ_0$ by embedding them into a possibly nonlinear parameter space. We illustrate our estimation procedure through simulations and empirical applications.

Problem

• Debiased Machine Learning
• High-dimensional Nuisance
• Moment Condition
• Riesz Representer
• Shape Constraints

Innovation

• Debiased Machine Learning
• Riesz representer
• Shape constraints
• High-dimensional nuisance parameters
• Moment condition