Structure Learning for Cyclic Linear Causal Models

Abstract

We consider the problem of structure learning for linear causal models based on observational data. We treat models given by possibly cyclic mixed graphs, which allow for feedback loops and effects of latent confounders. Generalizing related work on bow-free acyclic graphs, we assume that the underlying graph is simple. This entails that any two observed variables can be related through at most one direct causal effect and that (confounding-induced) correlation between error terms in structural equations occurs only in absence of direct causal effects. We show that, despite new subtleties in the cyclic case, the considered simple cyclic models are of expected dimension and that a previously considered criterion for distributional equivalence of bow-free acyclic graphs has an analogue in the cyclic case. Our result on model dimension justifies in particular score-based methods for structure learning of linear Gaussian mixed graph models, which we implement via greedy search.

A powerful test for differentially expressed gene pathways via graph-informed structural equation modeling

“…First, while T2-DAG requires that the auxiliary pathway information can be represented by a DAG, it is feasible to extend it to non-DAG pathways with more complex gene interactions. For example, the recently proposed linear SEM for cyclic mixed graphs (Améndola et al, 2020) provides a possible way to account for feedback loops and undirected edges in the gene pathway. Second, the proposed test assumes a diagonal covariance matrix R for the error term in (2).…”