Distributional equivalence and structure Learning for Bow-free Acyclic Path Diagrams

Christopher Nowzohour, Marloes H. Maathuis, Robin Evans, Peter Bühlmann

Abstract: We consider the problem of structure learning for bow-free acyclic path diagrams (BAPs). BAPs can be viewed as a generalization oflinear Gaussian DAG models that allow for certain hidden variables. We present a first method for this problem using a greedy score-basedsearch algorithm. We also prove some necessary and some sufficientconditions for distributional equivalence of BAPs which are used in analgorithmic approach to compute (nearly) equivalent model structures. This allows us to infer lower bounds of causal effects. We also presentapplications to real and simulated datasets using our publicly available R-package.