High-Dimensional Feature Selection for Sample Efficient Treatment Effect Estimation

TL;DR

This paper introduces a high-dimensional feature selection method for causal effect estimation that reduces sample complexity by identifying a sparse subset of relevant covariates, improving efficiency in observational studies.

Contribution

It proposes a nonconvex joint sparsity regularization approach that reliably recovers the relevant covariates under linear outcome models, enhancing sample efficiency.

Findings

Method accurately recovers relevant covariates with high probability.

Sample complexity scales with the size of the relevant subset and log of total covariates.

Experimental validation shows improved 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.