Primary Submission Category: Machine Learning and Causal Inference
Finite Sample Guarantees for Long Term, Dynamic, and Mediated Effects
Authors: Rahul Singh,
Presenting Author: Rahul Singh*
I study a rich class of longitudinal causal parameters such as long term, dynamic, and mediated effects. The class includes heterogeneous effects that vary according to subpopulation characteristics, as well as proximal effects defined in the presence of unobserved confounding. For machine learning estimators of these parameters, I construct and justify confidence intervals. Formally, as the first main result, I prove consistency, Gaussian approximation, and semiparametric efficiency when the machine learning estimators satisfy a few simple rate conditions. To demonstrate that the rate conditions are reasonable, I verify that they hold for adversarial estimators over several machine learning function spaces. Doing so requires the second main result: a mean square rate for nested nonparametric instrumental variable regression, which appears to be new, and which is of independent interest. A key feature of these results is a multiple robustness to ill posedness for proximal causal inference in longitudinal settings.