Doubly Robust Estimation with Machine Learning Predictions

The estimation of Average Treatment Effect (ATE) as a causal parameter is carried out in two steps, wherein the first step, the treatment, and outcome are modeled to incorporate the potential confounders, and in the second step, the predictions are inserted into the ATE estimators such as the Augmented Inverse Probability Weighting (AIPW) estimator. Due to the concerns regarding the nonlinear or unknown relationships between confounders and the treatment and outcome, there has been an interest in applying non-parametric methods such as Machine Learning (ML) algorithms instead. \cite{farrell2018deep} proposed to use two separate Neural Networks (NNs) where there's no regularization on the network's parameters except the Stochastic Gradient Descent (SGD) in the NN's optimization. Our simulations indicate that the AIPW estimator suffers extensively if no regularization is utilized. We propose the normalization of AIPW (referred to as nAIPW) which can be helpful in some scenarios. nAIPW, provably, has the same properties as AIPW, that is double-robustness and orthogonality \citep{chernozhukov2018double}. Further, if the first step algorithms converge fast enough, under regulatory conditions \citep{chernozhukov2018double}, nAIPW will be asymptotically normal.