Causal Inference on Distribution Functions

TL;DR

This paper introduces a new causal inference framework for outcomes represented as distribution functions in Wasserstein space, extending causal analysis beyond traditional Euclidean outcomes, with applications to health data.

Contribution

It develops doubly robust estimators and asymptotic theory for causal effects in Wasserstein space, a non-linear setting, which is a novel extension in causal inference.

Findings

Framework successfully quantifies causal effects on distributional outcomes.

Application to health data reveals insights into marriage's impact on activity patterns.

Method demonstrates robustness and theoretical soundness.

Abstract

Understanding causal relationships is one of the most important goals of modern science. So far, the causal inference literature has focused almost exclusively on outcomes coming from the Euclidean space $\mathbb{R}^p$. However, it is increasingly common that complex datasets are best summarized as data points in non-linear spaces. In this paper, we present a novel framework of causal effects for outcomes from the Wasserstein space of cumulative distribution functions, which in contrast to the Euclidean space, is non-linear. We develop doubly robust estimators and associated asymptotic theory for these causal effects. As an illustration, we use our framework to quantify the causal effect of marriage on physical activity patterns using wearable device data collected through the National Health and Nutrition Examination Survey.