A simple approach for finding the globally optimal Bayesian network structure

TL;DR

This paper introduces a simpler, more efficient algorithm for finding the globally optimal Bayesian network structure, capable of handling over 30 variables, and compares favorably to previous methods.

Contribution

The authors present a less complex, parallelizable algorithm that improves the efficiency of learning optimal Bayesian network structures for larger variable sets.

Findings

Able to learn optimal structures with over 30 variables

Outperforms previous state-of-the-art algorithms in efficiency

Provides open-source code and online demo

Abstract

We study the problem of learning the best Bayesian network structure with respect to a decomposable score such as BDe, BIC or AIC. This problem is known to be NP-hard, which means that solving it becomes quickly infeasible as the number of variables increases. Nevertheless, in this paper we show that it is possible to learn the best Bayesian network structure with over 30 variables, which covers many practically interesting cases. Our algorithm is less complicated and more efficient than the techniques presented earlier. It can be easily parallelized, and offers a possibility for efficient exploration of the best networks consistent with different variable orderings. In the experimental part of the paper we compare the performance of the algorithm to the previous state-of-the-art algorithm. Free source-code and an online-demo can be found at http://b-course.hiit.fi/bene.