Primary Submission Category: Machine Learning and Causal Inference
Finite-sample near-equivalences between Targeted Maximum Likelihood and Double Machine Learning (Augmented IPW)
Authors: Alejandro Schuler, David Bruns-Smith, Avi Feller,
Presenting Author: Alejandro Schuler*
Double machine learning (DML; a generalization of augmented inverse propensity score weighting) and Targeted Maximum Likelihood Estimation (TMLE) are two influence function-based estimators popular in causal inference, with extensive debates over the relative merits of each method. In this paper, we analyze their behavior in a large, well-studied class of estimands relevant to causal inference. We first review the known fact that a natural implementation of TMLE (TMLE with a “linear update”) for such estimands has a simple, closed form expression which is a minor variation of the DML estimator. We then present a new result that the DML estimator can also be written as a minor variation of the TMLE estimator. This establishes a finite-sample near-equivalence between DML and linear-update TMLE where the two are related by a single scaling factor. By analyzing the scaling factor we show that TMLE generally debiases the naive plugin estimate more aggressively than DML at the cost of inflating the debiasing weights and incurring more variance. Our results show that, for these estimands, DML can be interpreted as a “regularized” form of TMLE using the linear submodel, and confirm that the choice of submodel for TMLE can substantially impact its performance.