  Structure learning of Bayesian networks is an important problem that arises
in numerous machine learning applications. In this work, we present a novel
approach for learning the structure of Bayesian networks using the solution of
an appropriately constructed traveling salesman problem. In our approach, one
computes an optimal ordering (partially ordered set) of random variables using
methods for the traveling salesman problem. This ordering significantly reduces
the search space for the subsequent greedy optimization that computes the final
structure of the Bayesian network. We demonstrate our approach of learning
Bayesian networks on real world census and weather datasets. In both cases, we
demonstrate that the approach very accurately captures dependencies between
random variables. We check the accuracy of the predictions based on independent
studies in both application domains.
