Exploring the Role of Statistical Inference in Causal Discovery from Observational Data Sources

Posted: Feb 19, 2018

• Matthew Stewart
• Maya Foster
• Miles Turner

Abstract

This paper presents a novel framework for causal discovery that fundamentally reinterprets the relationship between statistical inference and causal reasoning in observational data. Traditional approaches to causal discovery often treat statistical methods as preliminary tools for identifying associations, with causal interpretation requiring additional assumptions or experimental validation. We propose an alternative paradigm where statistical inference itself becomes the primary mechanism for causal discovery through a novel integration of information-theoretic principles with topological data analysis. Our methodology introduces the concept of 'causal information geometry,' which characterizes the manifold structure of observational data spaces and identifies causal relationships through differential geometric properties of statistical manifolds. We demonstrate that causal directions can be inferred by analyzing the curvature and connectivity of these manifolds, providing a mathematically rigorous foundation for causal discovery that operates entirely within the observational domain. Through extensive experiments on synthetic and real-world datasets, we show that our approach achieves superior performance compared to existing methods in identifying causal structures, particularly in high-dimensional settings where traditional constraint-based and score-based methods struggle. The framework also naturally accommodates latent confounding and provides explicit measures of causal strength without requiring instrumental variables or other external aids. Our results challenge conventional wisdom about the limitations of observational data for causal inference and open new avenues for research at the intersection of statistics, geometry, and causal reasoning.