Latent factor models are increasingly popular for modeling multi-relational knowledge graphs. By their vectorial nature, it is not only hard to interpret why this class of models works so well, but also to understand where they fail and how they might be improved. We conduct an experimental survey of state-of-the-art models, not towards a purely comparative end, but as a means to get insight about their inductive abilities. To assess the strengths and weaknesses of each model, we create simple tasks that exhibit first, atomic properties of binary relations, and then, common inter-relational inference through synthetic genealogies. Based on these experimental results, we propose new research directions to improve on existing models.
Learning embeddings of entities and relations is an efficient and versatile method to perform machine learning on relational data such as knowledge graphs. In this work, we propose holographic embeddings (HolE) to learn compositional vector space representations of entire knowledge graphs. The proposed method is related to holographic models of associative memory in that it employs circular correlation to create compositional representations. By using correlation as the compositional operator HolE can capture rich interactions but simultaneously remains efficient to compute, easy to train, and scalable to very large datasets. In extensive experiments we show that holographic embeddings are able to outperform state-of-the-art methods for link prediction in knowledge graphs and relational learning benchmark datasets. Relational machine learning studies methods for the statistical analysis of relational, or graph-structured, data. In this paper, we provide a review of how such statistical models can be “trained” on large knowledge graphs, and then used to predict new facts about the world (which is equivalent to predicting new edges in the graph). In particular, we discuss two fundamentally different kinds of statistical relational models, both of which can scale to massive data sets. The first is based on latent feature models such as tensor factorization and multiway neural networks. The second is based on mining observable patterns in the graph. We also show how to combine these latent and observable models to get improved modeling power at decreased computational cost. Finally, we discuss how such statistical models of graphs can be combined with text-based information extraction methods for automatically constructing knowledge graphs from the Web. To this end, we also discuss Google's knowledge vault project as an example of such combination. In statistical relational learning, the link prediction problem is key to automatically understand the structure of large knowledge bases. As in previous studies, we propose to solve this problem through latent factorization. However, here we make use of complex valued embeddings. The composition of complex embeddings can handle a large variety of binary relations, among them symmetric and antisymmetric relations. Compared to state-of-the-art models such as Neural Tensor Network and Holographic Embeddings, our approach based on complex embeddings is arguably simpler, as it only uses the Hermitian dot product, the complex counterpart of the standard dot product between real vectors. Our approach is scalable to large datasets as it remains linear in both space and time, while consistently outperforming alternative approaches on standard link prediction benchmarks. We show the equivalence of two state-of-the-art link prediction knowledge graph completion methods: 's holographic embedding and 's complex embedding. We first consider a spectral version of the holographic embedding, exploiting the frequency domain in the Fourier transform for efficient computation. The analysis of the resulting method reveals that it can be viewed as an instance of the complex embedding with certain constraints cast on the initial vectors upon training. Conversely, any complex embedding can be converted to an equivalent holographic embedding. Embeddings of knowledge graphs have received significant attention due to their excellent performance for tasks like link prediction and entity resolution. In this short paper, we are providing a comparison of two state-of-the-art knowledge graph embeddings for which their equivalence has recently been established, i.e., ComplEx and HolE [Nickel, Rosasco, and Poggio, 2016; , 2016; Hayashi and Shimbo, 2017]. First, we briefly review both models and discuss how their scoring functions are equivalent. We then analyze the discrepancy of results reported in the original articles, and show experimentally that they are likely due to the use of different loss functions. In further experiments, we evaluate the ability of both models to embed symmetric and antisymmetric patterns. Finally, we discuss advantages and disadvantages of both models and under which conditions one would be preferable to the other.