Distributional Equivalence and Structure Learning for Bow-free Acyclic Path Diagrams
This work addresses structure learning in causal models with hidden variables, which is an incremental advancement in the field of causal inference.
The paper tackles the problem of structure learning for bow-free acyclic path diagrams (BAPs), which generalize linear Gaussian DAG models to include hidden variables, by presenting a first method using a greedy score-based search algorithm and proving conditions for distributional equivalence to infer lower bounds of causal effects, with applications to real and simulated datasets.
We consider the problem of structure learning for bow-free acyclic path diagrams (BAPs). BAPs can be viewed as a generalization of linear Gaussian DAG models that allow for certain hidden variables. We present a first method for this problem using a greedy score-based search algorithm. We also prove some necessary and some sufficient conditions for distributional equivalence of BAPs which are used in an algorithmic ap- proach to compute (nearly) equivalent model structures. This allows us to infer lower bounds of causal effects. We also present applications to real and simulated datasets using our publicly available R-package.