Asymmetric predictability in causal discovery: an information theoretic approach

2022/10/26 by Purkayastha, Soumik, Song, Peter X. K.
#Computation (stat.CO) #FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.2210.14455

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.

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