Embedding methods which enforce a partial order or lattice structure over the concept space, such as Order Embeddings (OE) (Vendrov et al., 2016), are a natural way to model transitive relational data (e.g. entailment graphs). However, OE learns a deterministic knowledge base, limiting expressiveness of queries and the ability to use uncertainty for both prediction and learning (e.g. learning from expectations). Probabilistic extensions of OE (Lai and Hockenmaier, 2017) have provided the ability to somewhat calibrate these denotational probabilities while retaining the consistency and inductive bias of ordered models, but lack the ability to model the negative correlations found in real-world knowledge. In this work we show that a broad class of models that assign probability measures to OE can never capture negative correlation, which motivates our construction of a novel box lattice and accompanying probability measure to capture anticorrelation and even disjoint concepts, while still providing the benefits of probabilistic modeling, such as the ability to perform rich joint and conditional queries over arbitrary sets of concepts, and both learning from and predicting calibrated uncertainty. We show improvements over previous approaches in modeling the Flickr and WordNet entailment graphs, and investigate the power of the model.

本文提出一种新的盒状晶格及其概率测度来捕捉反相关和不相交的概念，旨在克服Order Embeddings及其概率扩展无法建模现实世界知识中的负相关的问题。该方法不仅可以进行丰富的联合和条件查询，而且可以从预测中学习，并提高建模Flickr和WordNet蕴含图的能力。

基于Box Lattice Measures的知识图谱概率嵌入