Bayesian Network Structure Learning Using Quantum Annealing

TL;DR

This paper presents a novel approach to learning Bayesian network structures using quantum annealing by reformulating the problem into an Ising spin system, enabling efficient quantum optimization.

Contribution

It introduces a new pseudo-Boolean formulation for Bayesian network structure learning suitable for quantum annealing, requiring O(n^2) qubits and independent of data size.

Findings

Efficient reformulation of Bayesian network scoring as Ising model

Proved lower bounds on penalty term weights

Mapping is instance-independent for fixed variables

Abstract

We introduce a method for the problem of learning the structure of a Bayesian network using the quantum adiabatic algorithm. We do so by introducing an efficient reformulation of a standard posterior-probability scoring function on graphs as a pseudo-Boolean function, which is equivalent to a system of 2-body Ising spins, as well as suitable penalty terms for enforcing the constraints necessary for the reformulation; our proposed method requires $\mathcal O(n^2)$ qubits for $n$ Bayesian network variables. Furthermore, we prove lower bounds on the necessary weighting of these penalty terms. The logical structure resulting from the mapping has the appealing property that it is instance-independent for a given number of Bayesian network variables, as well as being independent of the number of data cases.