Structure Learning for Cyclic Linear Causal Models
This work addresses causal inference in systems with feedback, which is incremental by extending prior results from acyclic to cyclic graphs.
The paper tackles structure learning for linear causal models with cyclic mixed graphs, allowing for feedback loops and latent confounders, and shows that simple cyclic models have expected dimension, enabling score-based methods like greedy search.
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.