  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.
