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 approach 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.
"Distributional equivalence and structure learning for bow-free acyclic path diagrams." Electron. J. Statist. 11 (2) 5342 - 5374, 2017. https://doi.org/10.1214/17-EJS1372