Learning Bayesian Networks with Annealing Machine

Recent studies have reported that annealing machines are capable of solving combinatorial optimization problems with high accuracy. Annealing machines can potentially be applied to score-based Bayesian network structure learning. However, the bit capacity of an annealing machine is currently limited. To utilize the annealing technology, converting score-based learning problems into quadratic unconstrained binary optimizations within the bit capacity is necessary. In this paper, we propose an efficient conversion method with the advanced identification of candidate parent sets and their decomposition. We also provide an integer programming problem to find the decomposition that minimizes the number of required bits. Experimental results on $7$ benchmark datasets with variables from $75$ to $223$ show that our approach requires less bits than the $100$K bit capacity of the fourth-generation Fujitsu Digital Annealer, a fully coupled annealing machine developed with semiconductor technology. Moreover, we demonstrate that the Digital Annealer with our conversion method outperforms existing algorithms on score maximization. These results highlight the utility of annealing processors in learning Bayesian networks.