Probabilistic circuits (PCs) are a prominent representation of probability distributions with tractable inference. While parameter learning in PCs is rigorously studied, structure learning is often more based on heuristics than on principled objectives. In this paper, we develop Bayesian structure scores for deterministic PCs, i.e., the structure likelihood with parameters marginalized out, which are well known as rigorous objectives for structure learning in probabilistic graphical models. When used within a greedy cutset algorithm, our scores effectively protect against overfitting and yield a fast and almost hyper-parameter-free structure learner, distinguishing it from previous approaches. In experiments, we achieve good trade-offs between training time and model fit in terms of log-likelihood. Moreover, the principled nature of Bayesian scores unlocks PCs for accommodating frameworks such as structural expectation-maximization.

翻译：概率电路(PCs)是概率分布的显著表示,它具有可移动的推理力。虽然严格研究了PCs中的参数学习,但结构学习往往更多地基于重力学而不是原则性目标。在本文中,我们开发了确定型PCs的巴伊西亚结构分数,即边缘参数的结构分数,这是众所周知的在概率图形模型中进行结构学习的严格目标。当在贪婪的割裂算法中使用时,我们的分数有效地保护了不被过度配置,并产生了一个快速和几乎超度的无参数结构学习者,将其与以往的方法区分开来。在实验中,我们在培训时间和模型之间实现了良好的权衡,在日志相似性方面是合适的。此外,巴伊斯分数的有原则性性质为结构期待-最大化等通融框架打开了方便框架的方便性。