High-Dimensional Feature Selection for Sample Efficient Treatment Effect Estimation

Abstract

The estimation of causal treatment effects from observational data is a fundamental problem in causal inference. To avoid bias, the effect estimator must control for all confounders. Hence practitioners often collect data for as many covariates as possible to raise the chances of including the relevant confounders. While this addresses the bias, this has the side effect of significantly increasing the number of data samples required to accurately estimate the effect due to the increased dimensionality. In this work, we consider the setting where out of a large number of covariates $X$ that satisfy strong ignorability, an unknown sparse subset $S$ is sufficient to include to achieve zero bias, i.e. $c$-equivalent to $X$. We propose a common objective function involving outcomes across treatment cohorts with nonconvex joint sparsity regularization that is guaranteed to recover $S$ with high probability under a linear outcome model for $Y$ and subgaussian covariates for each of the treatment cohort. This improves the effect estimation sample complexity so that it scales with the cardinality of the sparse subset $S$ and $\log |X|$, as opposed to the cardinality of the full set $X$. We validate our approach with experiments on treatment effect estimation.

References in corpus (7)

• Nearly unbiased variable selection under minimax concave penalty
• Causal Effect Inference with Deep Latent-Variable Models
• A Survey of Learning Causality with Data: Problems and Methods
• Identification of Conditional Interventional Distributions
• Interval Estimation of Individual-Level Causal Effects Under Unobserved Confounding
• An Evaluation Toolkit to Guide Model Selection and Cohort Definition in Causal Inference
• DeepMatch: Balancing Deep Covariate Representations for Causal Inference Using Adversarial Training