What question did this study set out to answer?

The research aims to develop a geometric measure, the Causal Geodesic Gap (CGG), to quantify confounding in statistical models.

June 3, 2026Open Access

Causal Geodesic Gap (CGG): A Geometric Measure of Confounding via Fisher-Rao Distance

Key Points

The research aims to develop a geometric measure, the Causal Geodesic Gap (CGG), to quantify confounding in statistical models.
Utilized Fisher-Rao distance to compare observational and interventional distributions.
Integrated Amari's information geometry and Pearl's do-calculus for diagnostics.
Analyzed empirical data from the Enron email dataset using the reproducible pipeline.
Established CGG as a valid scalar measure for identifying confounding with clear parametrisation invariance.
Demonstrated application in real data analysis through the Enron dataset, reinforcing CGG's utility.
Highlighted potential improvements in confounding diagnostics using geometric measurements.

Abstract

Reproduction code for the manuscript "Causal Geodesic Gap (CGG): A Geometric Measure of Confounding via Fisher-Rao Distance" (Szalay 2026). The Causal Geodesic Gap (CGG) is a scalar measure quantifying the Fisher-Rao geodesic distance between the observational distribution P(Y|X=x) and its interventional counterpart P(Y|do(X=x)) on the statistical manifold. It combines Amari's information geometry with Pearl's do-calculus to provide a parametrisation-invariant diagnostic for confounding in structural causal models. This Jupyter notebook contains the complete reproduction pipeline accompanying the manuscript. The Enron empirical analysis requires emails.csv from the public Kaggle Enron dataset (https://www.kaggle.com/datasets/wcukierski/enron-email-dataset). Dependencies: numpy, pandas, scipy, networkx, matplotlib, scikit-learn.

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