A Traveling Salesman Learns Bayesian Networks

Abstract

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.

Dynamical Systems Theory and Algorithms for NP-hard Problems

“…In general, however, the distance matrix D = (d i j ) does not have to be symmetric (for example see [45]). The ordering σ can be represented as a unique permutation matrix P. Note, however, that due to the underlying cyclic symmetry, multiple orderings -corresponding to different permutation matriceshave the same cost.…”