Learning Linear Non-Gaussian Graphical Models with Multidirected Edges

TL;DR

This paper introduces a novel method for learning the structure of linear non-Gaussian graphical models, specifically incorporating multidirected edges to represent hidden common causes, using higher order cumulants.

Contribution

It extends existing algorithms by enabling the detection of multidirected edges, thus capturing complex hidden variable structures in acyclic mixed graphs.

Findings

Successfully recovers the correct graph structure with multidirected edges.

Utilizes higher order cumulants and the multi-trek rule for hidden cause detection.

Applicable to bow-free acyclic mixed graphs.

Abstract

In this paper we propose a new method to learn the underlying acyclic mixed graph of a linear non-Gaussian structural equation model given observational data. We build on an algorithm proposed by Wang and Drton, and we show that one can augment the hidden variable structure of the recovered model by learning {\em multidirected edges} rather than only directed and bidirected ones. Multidirected edges appear when more than two of the observed variables have a hidden common cause. We detect the presence of such hidden causes by looking at higher order cumulants and exploiting the multi-trek rule. Our method recovers the correct structure when the underlying graph is a bow-free acyclic mixed graph with potential multi-directed edges.