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

Soft Learning Probabilistic Circuits

Sum-Product Networks (SPNs) are a class of expressive yet tractable
hierarchical graphical models. LearnSPN is a structure learning algorithm for
SPNs that uses hierarchical co-clustering to simultaneously identifying similar
entities and similar features. The original LearnSPN algorithm assumes that all
the variables are discrete and there is no missing data. We introduce a
practical, simplified version of LearnSPN, MiniSPN, that runs faster and can
handle missing data and heterogeneous features common in real applications. We
demonstrate the performance of MiniSPN on standard benchmark datasets and on
two datasets from Google's Knowledge Graph exhibiting high missingness rates
and a mix of discrete and continuous features.

本研究介绍了一种名为 MiniSPN 的简化版本的 LearnSPN 算法，它可以快速地处理在实际应用中常见的缺失数据和异构特征，实验表明在两个具有高缺失率和混合离散和连续特征的 Google 知识图谱和标准基准数据集上 MiniSPN 表现良好。