Causal discovery of linear acyclic models with arbitrary distributions

TL;DR

This paper introduces a new method for discovering causal relationships in linear acyclic models with arbitrary distributions, overcoming limitations of previous approaches by combining independence tests and ICA.

Contribution

It generalizes and combines existing methods to accurately identify causal structures in cases where prior methods fail or provide limited information.

Findings

Exact graphical conditions for model equivalence

Method outperforms previous approaches in simulations

Effective for models with arbitrary distributions

Abstract

An important task in data analysis is the discovery of causal relationships between observed variables. For continuous-valued data, linear acyclic causal models are commonly used to model the data-generating process, and the inference of such models is a well-studied problem. However, existing methods have significant limitations. Methods based on conditional independencies (Spirtes et al. 1993; Pearl 2000) cannot distinguish between independence-equivalent models, whereas approaches purely based on Independent Component Analysis (Shimizu et al. 2006) are inapplicable to data which is partially Gaussian. In this paper, we generalize and combine the two approaches, to yield a method able to learn the model structure in many cases for which the previous methods provide answers that are either incorrect or are not as informative as possible. We give exact graphical conditions for when two distinct models represent the same family of distributions, and empirically demonstrate the power of our method through thorough simulations.