Learning huge Bayesian network structures by RAI algorithm with transitivity

Abstract

Learning Bayesian networks (BNs) is NP-hard. Recently, we can learn 1000 nodes BNs with consistency by the RAI algorithm using the Bayes factor, which is the state-of-the-art learning method. However, it is important to enable learning huger BNs to apply it in practice. This paper proves that conditional independence (CI) of BNs has the transitivity that can infer, from CI between a pair of variables, CI between each of them and another variable, and proposes a constraint-based algorithm, using the RAI algorithm with the transitivity. The experimental results show that the proposed method decreases the number of CI tests and run-time, and can learn huge BNs which prototypical constraint-based algorithms cannot learn.