Learning Linear Non-Gaussian Graphical Models with Multidirected Edges
This work addresses a specific challenge in causal discovery for researchers in statistics and machine learning, but it is incremental as it builds on an existing algorithm.
The paper tackles the problem of learning acyclic mixed graphs from observational data in linear non-Gaussian structural equation models by introducing multidirected edges to represent hidden common causes involving more than two variables, and it recovers the correct structure under specific graph conditions.
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.