Improved Acyclicity Reasoning for Bayesian Network Structure Learning with Constraint Programming

• URL: http://arxiv.org/abs/2106.12269v1
• Date: Wed, 23 Jun 2021 09:46:11 GMT
• Title: Improved Acyclicity Reasoning for Bayesian Network Structure Learning with Constraint Programming
• Authors: Fulya Tr\"osser (MIAT INRA), Simon de Givry (MIAT INRA), George Katsirelos (MIA-Paris)
• Abstract summary: Learning the structure of a Bayesian network (BNSL) from discrete data is known to be an NP-hard task. In this work, we propose a new time algorithm for discovering a subset of all possible cluster cuts. We show that, despite being suboptimal, they improve performance by orders of magnitude. The resulting solver also compares favourably with GOBNILP, a state-of-the-art solver for the BNSL problem.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Bayesian networks are probabilistic graphical models with a wide range of application areas including gene regulatory networks inference, risk analysis and image processing. Learning the structure of a Bayesian network (BNSL) from discrete data is known to be an NP-hard task with a superexponential search space of directed acyclic graphs. In this work, we propose a new polynomial time algorithm 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 programmingbased branch-and-bound solver CPBayes and show that, despite being suboptimal, they improve performance 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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