Improved Acyclicity Reasoning for Bayesian Network Structure Learning with Constraint ProgrammingDownload PDFOpen Website

27 Feb 2023OpenReview Archive Direct UploadReaders: Everyone
Abstract: Bayesian networks are probabilistic graphical mod- els with a wide range of application areas includ- ing gene regulatory networks inference, risk anal- ysis and image processing. Learning the structure of a Bayesian network (BNSL) from discrete data is known to be an NP-hard task with a superexpo- nential search space of directed acyclic graphs. In this work, we propose a new polynomial time algo- rithm for discovering a subset of all possible cluster cuts, a greedy algorithm for approximately solving the resulting linear program, and a generalised arc consistency algorithm for the acyclicity constraint. We embed these in the constraint programming- based branch-and-bound solver CPBayes and show that, despite being suboptimal, they improve per- formance by orders of magnitude. The resulting solver also compares favourably with GOBNILP, a state-of-the-art solver for the BNSL problem which solves an NP-hard problem to discover each cut and solves the linear program exactly.
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