Discovering Cyclic Causal Models by Independent Components Analysis

TL;DR

This paper extends ICA-based methods to discover linear non-Gaussian causal models that include cycles, providing algorithms and conditions for identifying stable models in complex causal structures.

Contribution

It generalizes previous acyclic models to include cyclic causal structures and introduces conditions for identifying unique stable models.

Findings

Successfully applied to simulated data

Provides sufficient conditions for model stability

Extends LiNGAM to cyclic causal models

Abstract

We generalize Shimizu et al's (2006) ICA-based approach for discovering linear non-Gaussian acyclic (LiNGAM) Structural Equation Models (SEMs) from causally sufficient, continuous-valued observational data. By relaxing the assumption that the generating SEM's graph is acyclic, we solve the more general problem of linear non-Gaussian (LiNG) SEM discovery. LiNG discovery algorithms output the distribution equivalence class of SEMs which, in the large sample limit, represents the population distribution. We apply a LiNG discovery algorithm to simulated data. Finally, we give sufficient conditions under which only one of the SEMs in the output class is 'stable'.