Probabilistic Circuits (PCs) are prominent tractable probabilistic models, allowing for a range of exact inferences. This paper focuses on the main algorithm for training PCs, LearnSPN, a gold standard due to its efficiency, performance, and ease of use, in particular for tabular data. We show that LearnSPN is a greedy likelihood maximizer under mild assumptions. While inferences in PCs may use the entire circuit structure for processing queries, LearnSPN applies a hard method for learning them, propagating at each sum node a data point through one and only one of the children/edges as in a hard clustering process. We propose a new learning procedure named SoftLearn, that induces a PC using a soft clustering process. We investigate the effect of this learning-inference compatibility in PCs. Our experiments show that SoftLearn outperforms LearnSPN in many situations, yielding better likelihoods and arguably better samples. We also analyze comparable tractable models to highlight the differences between soft/hard learning and model querying.

PC模型是具有范围完全推理能力的显著可计算的概率模型，该论文主要关注用于训练PC模型的主要算法LearnSPN，我们提出了一种名为SoftLearn的新的学习过程，通过软聚类过程诱导出一个PC模型，实验证明SoftLearn在许多情况下优于LearnSPN，产生更好的似然和样本，我们还分析了可比较的可计算模型来突显软/硬学习和模型查询之间的差异。

软学习概率电路