Bayesian Network Structure Learning Using Quantum Annealing
This work addresses structure learning in Bayesian networks for probabilistic modeling, but it is incremental as it adapts existing quantum methods to this specific task.
The authors tackled the problem of learning Bayesian network structures by reformulating a scoring function into a pseudo-Boolean form compatible with quantum annealing, requiring O(n^2) qubits for n variables and proving lower bounds on penalty weights.
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.