A novel Bayesian Network structure learning algorithm based on minimal correlated itemset mining techniques

In this paper, we propose a new constraint-based method for Bayesian network structure learning based on correlated itemset mining techniques. The aim of this method is to identify and to represent conjunctions of Boolean factors implied in probabilistic dependence relationships, that may be ignored by constraint and scoring-based learning proposals when the pairwise dependencies are weak (e.g., noisy- XOR). The method is also able to identify some specific (almost) deterministic relationships in the data that cause the violation of the faithfulness assumption on which are based most constraint-based methods. The algorithm operates in two steps: (1) extraction of minimal supported and correlated itemsets, and (2), construction of the structure by extracting the most significant association rules in these itemsets. The method is illustrated on a simple but realistic benchmark plaguing the standard scoring and constraint- based algorithms.