Geodesic Causal Inference

Music City Center 

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. Causal inference has been developed mainly for regression relationships with scalar responses and also for distributional responses. We introduce here a general framework for causal inference when responses 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 Fréchet 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 study uncertainty quantification and inference for the treatment effect. Examples and practical implementations include simulations and data illustrations for responses corresponding to compositional responses as encountered for U.S. statewise energy source data, where we study the effect of coal mining, network data corresponding to New York taxi trips, where the effect of the COVID-19 pandemic is of interest, and the studying the effect of Alzheimer's disease on connectivity networks.

Doubly robust estimation

Fréchet regression

geodesic average treatment effect

metric statistic

network

random object 

IMS