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.

翻译：近期研究报告指出，退火机能够以高精度解决组合优化问题。退火机有望应用于基于评分的贝叶斯网络结构学习，然而当前退火机的位容量存在局限。为运用退火技术，需在限定位容量内将基于评分的学习问题转化为无约束二次二进制优化问题。本文提出一种高效的转化方法，通过候选父集的高级识别及其分解策略实现。同时给出一个整数规划问题，旨在寻找使所需位数最小化的分解方案。在包含75至223个变量的7个基准数据集上的实验结果表明，该方法所需位数低于第四代富士通数字退火器（采用半导体技术开发的全耦合退火机）的10万位容量。此外，我们证明采用该转化方法的数字退火器在评分最大化方面优于现有算法。这些结果凸显了退火处理器在贝叶斯网络学习中的实用性。