Learning Bayesian Networks based on Order Graph with Ancestral Constraints

We consider incorporating ancestral constraints into structure learning for Bayesian Networks (BNs) when executing an exact search based on order graph; this is thought to be impossible because ancestral constraints are non-decomposable. In order to adapt to the constraints, the node in an Order Graph (OG) is generalized as a series of directed acyclic graphs (DAGs). Then, we design a novel revenue function to breed out infeasible and suboptimal nodes to expedite the graph search. A breadth-first search algorithm is implemented in the new search space, verifying the validity and efficiency of the proposed framework. It has been demonstrated that, when the ancestral constraints are consistent with the ground-truth network or deviate from it, the new framework can navigate a path that leads to a global optimization in almost all cases with less time and space required for orders of magnitude than the state-of-the-art framework, such as EC-Tree.