Probabilistic models of relational implication

Knowledge bases and relational data form a powerful ontological framework for representing world knowledge. Relational data in its most basic form is a static collection of known facts. However, by learning to infer and deduct additional information and structure, we can massively increase the expressibility, generality, and usefulness of the underlying data. One common form of inferential reasoning in knowledge bases is implication discovery. Here, by learning when one relation implies another, we can implicitly extend our knowledge representation. There are several existing models for relational implication, however we argue they are sufficiently motivated but not entirely principled. To this end, we define a formal probabilistic model of relational implication. By using estimators based on the empirical distribution of our dataset, we demonstrate that our model outperforms existing approaches. While previous work achieves a best score of 0 . 7812 AUC on an evaluatory dataset, our ProbE model improves this to 0 . 7915 . Furthermore, we demonstrate that our model can be improved substantially through the use of link prediction models and dense latent representations of the underlying argument and relations. This variant, denoted ProbL, improves the state of the art on our evaluatoin dataset to 0 . 8143 . In addition to developing a new framework and providing novel scores of relational implication, we provide two pragmatic resources to assist future research. First, we motivate and develop an improved crowd framework for constructing labelled datasets of relational implication. Using this, we reannotate and make public a dataset comprised of 17 , 848 instances of labelled relational implication. We demonstrate that precision (as evaluated by expert consensus with the crowd labels) on the resulting dataset improves from 53 % to 95 %. We also argue that current implementations of link prediction models are not sufficiently scalable or parametisable. We provide a highly optimised and parallelised framework for the development and hyperparameter tuning of link prediction models, along with an implementation of a number of existing approaches.