# Causal Inference on Distribution Functions

arXiv: https://arxiv.org/abs/2101.01599 · HTML: https://mlsanity.com/paper/2101.01599/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Jan 2021.

## Built on by (most cited first, 11 of 11)

- [Doubly robust estimation of causal effects for random object outcomes with continuous treatments](https://mlsanity.com/paper/2506.22754/) (2025)
- [Kernel-based estimators for functional causal effects](https://mlsanity.com/paper/2503.05024/) (2025)
- [Moments of Causal Effects](https://mlsanity.com/paper/2505.04971/) (2025)
- [Interpretable Causal Inference for Analyzing Wearable, Sensor, and Distributional Data](https://mlsanity.com/paper/2312.10569/) (2023)
- [A primer on optimal transport for causal inference with observational data](https://mlsanity.com/paper/2503.07811/) (2025)
- [Wasserstein Transfer Learning](https://mlsanity.com/paper/2505.17404/) (2025)
- [The Causal Impact of Credit Lines on Spending Distributions](https://mlsanity.com/paper/2312.10388/) (2023)
- [A Semiparametric Approach to Causal Inference](https://mlsanity.com/paper/2411.00950/) (2024)
- [Fr'echet Geodesic Boosting](https://mlsanity.com/paper/2509.18013/) (2025)
- [Toward an Asymptotic Efficiency Theory on Regular Parameter Manifolds](https://mlsanity.com/paper/2510.13703/) (2025)
- [Wasserstein Policy Learning for Distributional Outcomes](https://mlsanity.com/paper/2606.19117/) (2026)

## Abstract (arXiv)

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 ℝp. 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.