De-Biased Machine Learning of Global and Local Parameters Using Regularized Riesz Representers

TL;DR

This paper introduces adaptive inference methods using $\,ell_1$ regularization and Riesz representers for estimating both regular and non-regular linear functionals of the conditional expectation function, providing valid confidence bands.

Contribution

It develops a novel Neyman orthogonal approach incorporating Riesz representers for robust, honest inference on complex functionals in semi-parametric and nonparametric models.

Findings

Provides non-asymptotic, uniform valid confidence bands

Achieves weak double sparsity robustness between regression and representer approximations

Ensures asymptotic validity over large model classes

Abstract

We provide adaptive inference methods, based on $\ell_1$ regularization, for regular (semi-parametric) and non-regular (nonparametric) linear functionals of the conditional expectation function. Examples of regular functionals include average treatment effects, policy effects, and derivatives. Examples of non-regular functionals include average treatment effects, policy effects, and derivatives conditional on a covariate subvector fixed at a point. We construct a Neyman orthogonal equation for the target parameter that is approximately invariant to small perturbations of the nuisance parameters. To achieve this property, we include the Riesz representer for the functional as an additional nuisance parameter. Our analysis yields weak ``double sparsity robustness'': either the approximation to the regression or the approximation to the representer can be ``completely dense'' as long as the other is sufficiently ``sparse''. Our main results are non-asymptotic and imply asymptotic uniform validity over large classes of models, translating into honest confidence bands for both global and local parameters.