# Geodesic Causal Inference

arXiv: https://arxiv.org/abs/2406.19604 · HTML: https://mlsanity.com/paper/2406.19604/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Jun 2024.

## Built on by (most cited first, 7 of 7)

- [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)
- [SphUnc: Hyperspherical Uncertainty Decomposition and Causal Identification via Information Geometry](https://mlsanity.com/paper/2603.01168/) (2026)
- [Fr'echet Geodesic Boosting](https://mlsanity.com/paper/2509.18013/) (2025)
- [Causal Representation Learning with Optimal Compression under Complex Treatments](https://mlsanity.com/paper/2603.11907/) (2026)
- [Wasserstein Policy Learning for Distributional Outcomes](https://mlsanity.com/paper/2606.19117/) (2026)
- [Causal inference for group-contaminated structured outcomes: observable quotients, lossless reduction and exact randomization inference](https://mlsanity.com/paper/2608.11954/) (2026)

## Abstract (arXiv)

Adjusting for confounding and imbalance when establishing statistical relationships is an increasingly important task, and causal inference methods have emerged as the most popular tool to achieve this. Existing methodology has been developed primarily for outcomes that lie in Euclidean spaces. We introduce here a general framework for causal inference when outcomes reside in general geodesic metric spaces, where we draw on a novel geodesic calculus that facilitates scalar multiplication for geodesics and the quantification of treatment effects through the concept of geodesic average treatment effect. Using ideas from Fr'echet regression, we obtain a doubly robust estimation of the geodesic average treatment effect and results on consistency and rates of convergence for the proposed estimators. We also develop an intrinsic uncertainty quantification framework for the treatment effect based on Fr'echet objective functions. The proposed framework is illustrated through simulations and real data applications, including network-valued outcomes from New York City taxi trips to assess the impact of the COVID-19 pandemic, and compositional data on U.S. state-level energy sources to study the effect of coal mining.