This problem, chordal Markov network structure learning (CMSL), is computationally notoriously challenging; e.g., finding a maximum likelihood chordal Markov network

The authors present a branch and bound algorithm for learning Chordal Markov networks. The prior state of the art algorithm is a dynamic programming approach based on a recursive characterization of clique tress and storing in memory the scores of already-solved subproblems. The proposed algorithm uses a branch and bound algorithm to search for an optimal chordal Markov network. The algorithm first uses a dynamic programming algorithm to enumerate Bayesian network structures, which are later used as pruning bounds. A symmetry breaking technique is introduced to prune the search space.

This problem, chordal Markov network structure learning (CMSL), is computationally notoriously challenging; e.g., finding a maximum likelihood chordal Markov network

We present a new algorithmic approach for the task of finding a chordal Markov network structure that maximizes a given scoring function. The algorithm is based on branch and bound and integrates dynamic programming for both domain pruning and for obtaining strong bounds for search-space pruning. Empirically, we show that the approach dominates in terms of running times a recent integer programming approach (and thereby also a recent constraint optimization approach) for the problem.