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

2025-08-11

AI Summary

Traditional causal inference is constrained by a binary paradigm—“observation vs. intervention”—which fails to model intermediate intervention intensities and lacks a continuous quantification framework for causal effects. Method: We propose a continuous causal modeling paradigm, introducing the concept of “causal geodesics”: shortest smooth paths from observational to interventional distributions in a probability distribution metric space. Counterfactual effects are defined via pathwise differentiation along these geodesics, and path modeling and effect estimation are realized through distributional interpolation and tools from differential geometry. Contribution: This work establishes, for the first time, a continuous causal effect quantification framework bridging observability and intervenability. It enables interpretable modeling and estimation of causal effects under arbitrary (including partial or graded) interventions, thereby relaxing the standard discrete-intervention assumption. The framework provides a novel theoretical foundation and computational pathway for causal discovery, incremental policy evaluation, and robust causal inference.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Knowledge Representation and Reasoning: Action, Change, and Causality

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• Studying stochastic interventions between correlation and causation
• Defining paths interpolating treatment density and target intervention
• Interpreting causal effects along geodesic paths

Innovation

• Smooth distribution paths interpolate treatment and target
• Geodesic metric defines shortest counterfactual intervention path
• Framework bridges observational correlation to causal intervention