A Gaussian Process Framework for Overlap and Causal Effect Estimation with High-Dimensional Covariates

Ghosh Debashis () and Cruz Cortés Efrén ()
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Ghosh Debashis: Department of Biostatistics and Informatics, 144805Colorado School of Public Health, 80045Aurora, CO, United States
Cruz Cortés Efrén: Department of Biostatistics and Informatics, 144805Colorado School of Public Health, 80045Aurora, CO, United States

Journal of Causal Inference, 2019, vol. 7, issue 2, 13

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 under a focused framework the stringency that accompanies the use of the treatment positivity assumption in high-dimensional settings.

Keywords: Average causal effect; Covariate balance; Functional data; Machine learning; Positivity (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:bpj:causin:v:7:y:2019:i:2:p:13:n:1

DOI: 10.1515/jci-2018-0024

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