RelWalk -- A Latent Variable Model Approach to Knowledge Graph Embedding

Knowledge Graph Embedding (KGE) is the task of jointly learning entity and relation embeddings for a given knowledge graph. Existing methods for learning KGEs can be seen as a two-stage process where (a) entities and relations in the knowledge graph are represented using some linear algebraic structures (embeddings), and (b) a scoring function is defined that evaluates the strength of a relation that holds between two entities using the corresponding relation and entity embeddings. Unfortunately, prior proposals for the scoring functions in the first step have been heuristically motivated, and it is unclear as to how the scoring functions in KGEs relate to the generation process of the underlying knowledge graph. To address this issue, we propose a generative account of the KGE learning task. Specifically, given a knowledge graph represented by a set of relational triples (h, R, t), where the semantic relation R holds between the two entities h (head) and t (tail), we extend the random walk model (Arora et al., 2016a) of word embeddings to KGE. We derive a theoretical relationship between the joint probability p(h, R, t) and the embeddings of h, R and t. Moreover, we show that marginal loss minimisation, a popular objective used by much prior work in KGE, follows naturally from the log-likelihood ratio maximisation under the probabilities estimated from the KGEs according to our theoretical relationship. We propose a learning objective motivated by the theoretical analysis to learn KGEs from a given knowledge graph. The KGEs learnt by our proposed method obtain state-of-the-art performance on FB15K237 and WN18RR benchmark datasets, providing empirical evidence in support of the theory.