A Traveling Salesman Learns Bayesian Networks

TL;DR

This paper introduces a novel method for learning Bayesian network structures by transforming the problem into a traveling salesman problem, enabling more efficient and accurate dependency modeling in real-world datasets.

Contribution

It presents a new approach that uses TSP solutions to determine variable orderings, reducing search space and improving Bayesian network structure learning.

Findings

Accurately captures dependencies in census and weather datasets

Reduces search space for Bayesian network structure learning

Demonstrates high prediction accuracy in real-world applications

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.