Causal Geodesy: Counterfactual Estimation Along the Path Between Correlation and Causation

TL;DR

This paper introduces causal geodesy, a framework for analyzing stochastic interventions that interpolate between observational data and specific counterfactual scenarios, using geodesic paths in distribution space.

Contribution

It proposes a novel framework for studying intermediate interventions between correlation and causation via distributional geodesics.

Findings

Defines paths of distributions between observational and counterfactual worlds.

Introduces the concept of geodesic paths for causal effect estimation.

Provides methods for interpreting and estimating effects along these paths.

Abstract

We introduce causal geodesy, a framework for studying the landscape of stochastic interventions that lie between the two extremes of performing no intervention, and performing a sharp intervention that sets an exposure equal to a specific value. We define this framework by constructing paths of distributions that smoothly interpolate between the treatment density and a point mass at the target intervention. Thus, each path starts at a purely observational (or correlational) quantity and moves into a counterfactual world. Of particular interest are paths that correspond to geodesics in some metric, i.e. the shortest path. We then consider the interpretation and estimation of the corresponding causal effects as we move along the path from correlation toward causation.