Reconstructing Bayesian Networks on a Quantum Annealer

TL;DR

This paper implements and evaluates a quantum annealing approach for learning Bayesian network structures, demonstrating its effectiveness on small problems and proposing a divide et impera strategy for larger instances.

Contribution

It provides a Python implementation of O'Gorman's quantum annealing algorithm and introduces a divide et impera method to scale to larger problems.

Findings

Effective for small-sized BNSL problems

Divide et impera approach outperforms direct implementation

Empirical results validate the proposed methods

Abstract

Bayesian networks are widely used probabilistic graphical models, whose structure is hard to learn starting from the generated data. O'Gorman et al. have proposed an algorithm to encode this task, i.e., the Bayesian network structure learning (BSNL), into a form that can be solved through quantum annealing, but they have not provided an experimental evaluation of it. In this paper, we present (i) an implementation in Python of O'Gorman's algorithm, (ii) a divide et impera approach that allows addressing BNSL problems of larger sizes in order to overcome the limitations imposed by the current architectures, and (iii) their empirical evaluation. Specifically, several problems with an increasing number of variables have been used in the experiments. The results have shown the effectiveness of O'Gorman's formulation for BNSL instances of small sizes, and the superiority of the divide et impera approach on the direct execution of O'Gorman's algorithm.