The Bias-Variance Tradeoff of Doubly Robust Estimator with Targeted $L_1$ regularized Neural Networks Predictions

TL;DR

This paper investigates how to tune neural network hyperparameters for doubly robust ATE estimation to balance bias and variance, especially in the presence of confounders and instrumental variables, using simulation results.

Contribution

It provides guidance on hyperparameter tuning of neural networks to improve doubly robust ATE estimation under complex confounding scenarios.

Findings

Proper neural network tuning reduces bias and variance in ATE estimates.

Avoiding perfect predictions in treatment models prevents positivity violations.

Simulation results offer practical recommendations for neural network employment.

Abstract

The Doubly Robust (DR) estimation of ATE can be carried out in 2 steps, where in the first step, the treatment and outcome are modeled, and in the second step the predictions are inserted into the DR estimator. The model misspecification in the first step has led researchers to utilize Machine Learning algorithms instead of parametric algorithms. However, 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 DR estimators. Thus the ML algorithms must be controlled to avoid perfect predictions for the treatment model while still learn the relationship between the confounders and the treatment and outcome. We use two Neural network architectures and investigate how their hyperparameters should be tuned in the presence of confounders and IVs to achieve a low bias-variance tradeoff for ATE estimators such as DR estimator. Through simulation results, we will provide recommendations as to how NNs can be employed for ATE estimation.