Sum-product networks (SPNs) are probabilistic models characterized by exact
and fast evaluation of fundamental probabilistic operations. Its superior
computational tractability has led to applications in many fields, such as
machine learning with time constraints or accuracy requirements and real-time
systems. The structural constraints of SPNs supporting fast inference, however,
lead to increased learning-time complexity and can be an obstacle to building
highly expressive SPNs. This study aimed to develop a Bayesian learning
approach that can be efficiently implemented on large-scale SPNs. We derived a
new full conditional probability of Gibbs sampling by marginalizing multiple
random variables to expeditiously obtain the posterior distribution. The
complexity analysis revealed that our sampling algorithm works efficiently even
for the largest possible SPN. Furthermore, we proposed a hyperparameter tuning
method that balances the diversity of the prior distribution and optimization
efficiency in large-scale SPNs. Our method has improved learning-time
complexity and demonstrated computational speed tens to more than one hundred
times faster and superior predictive performance in numerical experiments on
more than 20 datasets.

通过导出一种新的 Gibbs 采样的全部条件概率，通过边际化多个随机变量来快速获得后验分布，我们提出了一种可用于大规模 sum-product networks 的贝叶斯学习方法，同时还提出了一种超参数调优方法，通过在大规模 sum-product networks 中平衡先验分布的多样性和优化效率，改进了学习时间复杂度，并在超过 20 个数据集的数值实验中展示出了十倍到一百倍以上的计算速度和优秀的预测性能。