A Gaussian process framework for overlap and causal effect estimation with high-dimensional covariates

TL;DR

This paper introduces a Gaussian process approach for estimating causal effects in observational studies with high-dimensional covariates, highlighting the limitations of traditional overlap assumptions and proposing a data-adaptive alternative.

Contribution

It demonstrates the restrictive nature of overlap assumptions in high-dimensional settings and proposes a flexible Gaussian process framework with a data-adaptive strategy for causal effect estimation.

Findings

Overlap assumptions are highly restrictive with high-dimensional covariates.

Gaussian process models can characterize covariate distributions using RKHS theory.

A data-adaptive method for causal effect estimation that does not rely on strict overlap.

Abstract

A powerful tool for the analysis of nonrandomized observational studies has been the potential outcomes model. Utilization of this framework allows analysts to estimate average treatment effects. This article considers the situation in which high-dimensional covariates are present and revisits the standard assumptions made in causal inference. We show that by employing a flexible Gaussian process framework, the assumption of strict overlap leads to very restrictive assumptions about the distribution of covariates, results for which can be characterized using classical results from Gaussian random measures as well as reproducing kernel Hilbert space theory. In addition, we propose a strategy for data-adaptive causal effect estimation that does not rely on the strict overlap assumption. These findings reveal the stringency that accompanies the use of the treatment positivity assumption in high-dimensional settings.