Targeted <i>L</i>₁-Regularization and Joint Modeling of Neural Networks for Causal Inference

Abstract

The calculation of the Augmented Inverse Probability Weighting (AIPW) estimator of the Average Treatment Effect (ATE) is carried out in two steps, where in the first step, the treatment and outcome are modeled, and in the second step, the predictions are inserted into the AIPW estimator. The model misspecification in the first step has led researchers to utilize Machine Learning algorithms instead of parametric algorithms. However, the existence of strong confounders and/or Instrumental Variables (IVs) can lead the complex ML algorithms to provide perfect predictions for the treatment model which can violate the positivity assumption and elevate the variance of AIPW estimators. Thus the complexity of ML algorithms must be controlled to avoid perfect predictions for the treatment model while still learning the relationship between the confounders and the treatment and outcome. We use two NN architectures with an L1-regularization on specific NN parameters and investigate how their certain hyperparameters should be tuned in the presence of confounders and IVs to achieve a low bias-variance tradeoff for ATE estimators such as AIPW estimator. Through simulation results, we will provide recommendations as to how NNs can be employed for ATE estimation.

Keywords

• causal Inference
• instrumental variables
• neural networks
• doubly robust estimation
• regularization