Asymmetric predictability in causal discovery: an information theoretic approach

TL;DR

This paper introduces an information geometric framework for causal discovery based on predictive asymmetry, utilizing a new metric called Directed Mutual Information (DMI) to infer causal directions in observational data.

Contribution

It proposes a novel DMI metric for detecting causal directions, with scalable non-parametric estimation and proven statistical properties, advancing causal inference methods.

Findings

DMI effectively detects complex non-linear causal relations.

The method is computationally faster than classical density estimation.

Simulation and real data demonstrate DMI's accuracy in causal inference.

Abstract

Causal investigations in observational studies pose a great challenge in research where randomized trials or intervention-based studies are not feasible. We develop an information geometric causal discovery and inference framework of "predictive asymmetry". For $(X, Y)$, predictive asymmetry enables assessment of whether $X$ is more likely to cause $Y$ or vice-versa. The asymmetry between cause and effect becomes particularly simple if $X$ and $Y$ are deterministically related. We propose a new metric called the Directed Mutual Information ($DMI$) and establish its key statistical properties. $DMI$ is not only able to detect complex non-linear association patterns in bivariate data, but also is able to detect and infer causal relations. Our proposed methodology relies on scalable non-parametric density estimation using Fourier transform. The resulting estimation method is manyfold faster than the classical bandwidth-based density estimation. We investigate key asymptotic properties of the $DMI$ methodology and a data-splitting technique is utilized to facilitate causal inference using the $DMI$. Through simulation studies and an application, we illustrate the performance of $DMI$.