Normalized Augmented Inverse Probability Weighting with Neural Network Predictions

Area of Science:

• Causal inference
• Machine learning in statistics
• Econometrics

Background:

• Estimating average treatment effect (ATE) involves modeling confounders for treatment and outcome.
• Non-parametric machine learning (ML) methods are increasingly used due to complex confounder relationships.
• Standard augmented inverse probability weighting (AIPW) estimator is sensitive to regularization.

Purpose of the Study:

• To investigate the performance of the AIPW estimator when using machine learning algorithms without regularization.
• To propose a normalized version of AIPW (nAIPW) that retains desirable statistical properties.
• To compare the performance of AIPW and nAIPW under L1 regularization.

Main Methods:

• Simulations were conducted to evaluate the AIPW estimator's performance without regularization.
• A novel method, normalization of AIPW (nAIPW), was developed and theoretically analyzed.
• The study compared bias and variance of AIPW and nAIPW using neural networks with L1 regularization.

Main Results:

• The standard AIPW estimator significantly degrades without regularization.
• nAIPW provably maintains the double-robustness and orthogonality properties of AIPW.
• Under regularization, nAIPW demonstrates improved performance compared to unregularized AIPW.

Conclusions:

• Regularization is crucial for the reliable application of AIPW with machine learning models.
• nAIPW offers a robust alternative that preserves key theoretical properties.
• The proposed nAIPW method enhances the stability and accuracy of ATE estimation in complex scenarios.