De-Biased Machine Learning of Global and Local Parameters Using Regularized Riesz Representers
This work addresses inference challenges in causal and policy analysis, offering robust methods for researchers and practitioners, though it appears incremental by building on existing regularization and orthogonalization techniques.
The paper tackles the problem of adaptive inference for both regular and non-regular linear functionals, such as average treatment effects, by developing methods based on ℓ1 regularization and Neyman orthogonal equations. It achieves weak double sparsity robustness, allowing for honest confidence bands with non-asymptotic results that imply asymptotic uniform validity.
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.