Convolutional neural networks for valid and efficient causal inference

TL;DR

This paper explores using convolutional neural networks to improve causal inference by accurately modeling nuisance functions with time-structured covariates, ensuring valid and efficient estimation of treatment effects.

Contribution

It introduces a CNN-based approach for nuisance modeling in causal inference, providing theoretical convergence rates and demonstrating practical effectiveness through simulations and real data.

Findings

CNN achieves favorable convergence rates for nuisance models.

The proposed estimator provides valid and efficient causal effect estimates.

Empirical results show improved performance over existing methods.

Abstract

Convolutional neural networks (CNN) have been successful in machine learning applications. Their success relies on their ability to consider space invariant local features. We consider the use of CNN to fit nuisance models in semiparametric estimation of the average causal effect of a treatment. In this setting, nuisance models are functions of pre-treatment covariates that need to be controlled for. In an application where we want to estimate the effect of early retirement on a health outcome, we propose to use CNN to control for time-structured covariates. Thus, CNN is used when fitting nuisance models explaining the treatment and the outcome. These fits are then combined into an augmented inverse probability weighting estimator yielding efficient and uniformly valid inference. Theoretically, we contribute by providing rates of convergence for CNN equipped with the rectified linear unit activation function and compare it to an existing result for feedforward neural networks. We also show when those rates guarantee uniformly valid inference. A Monte Carlo study is provided where the performance of the proposed estimator is evaluated and compared with other strategies. Finally, we give results on a study of the effect of early retirement on hospitalization using data covering the whole Swedish population.