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How to Turn Your Knowledge Graph Embeddings into Generative Models via Probabilistic Circuits

2023-05-25 11:30:27
Lorenzo Loconte, Nicola Di Mauro, Robert Peharz, Antonio Vergari

Abstract

Some of the most successful knowledge graph embedding (KGE) models for link prediction -- CP, RESCAL, TuckER, ComplEx -- can be interpreted as energy-based models. Under this perspective they are not amenable for exact maximum-likelihood estimation (MLE), sampling and struggle to integrate logical constraints. This work re-interprets the score functions of these KGEs as circuits -- constrained computational graphs allowing efficient marginalisation. Then, we design two recipes to obtain efficient generative circuit models by either restricting their activations to be non-negative or squaring their outputs. Our interpretation comes with little or no loss of performance for link prediction, while the circuits framework unlocks exact learning by MLE, efficient sampling of new triples, and guarantee that logical constraints are satisfied by design. Furthermore, our models scale more gracefully than the original KGEs on graphs with millions of entities.

Abstract (translated)

这些最成功的知识图嵌入(KGE)模型——CP、RESCAL、TuckER、ComplEx——可以被解释为基于能量模型的模型。从这个角度来看,这些模型并不适合进行精确的最大似然估计(MLE)、采样和集成逻辑约束。这项工作重新解释这些KGE的得分函数,将其解释为电路——具有约束的计算图,可以高效地分配。然后,我们设计了两个食谱,通过限制其激活值是非负或平方其输出,获得高效的生成电路模型。我们的解释对于链接预测没有或几乎没有损失,而电路框架解锁MLE的学习,高效地采样新的三元组,并保证设计所满足的逻辑约束。此外,我们模型在具有数百万实体的Graph上比原始的KGE模型更加平滑地扩展。

URL

https://arxiv.org/abs/2305.15944

PDF

https://arxiv.org/pdf/2305.15944.pdf


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