Estimating Propensity Scores with Deep Adaptive Variable Selection

Abstract

The proliferation of observational data demands the development of statistical methods for causal inference. Many widely used causal inference methods are based on the propensity score. When estimating the propensity score, one essential question is which covariates should be included in the model. In this paper, we propose a deep adaptive variable selection based propensity score method (DAVSPS) by using representation learning and adaptive group LASSO. The key idea of DAFSPS is to combine the data-driven learning capability of representation learning and variable selection consistency of adaptive group LASSO to improve the estimation of the propensity score by selecting confounders and adjustment variables while removing instrumental and spurious variables. We also provide a detailed theoretical analysis to prove the variable selection consistency of DAVSPS. We evaluate the performance of our method on simulated data to demonstrate its superiority over state-of-the-art methods and apply it to real data.Keywordscausal inferencepropensity scorevariable selectionadaptive LASSOconsistency