In statistical relational learning, knowledge graph completion deals with automatically understanding the structure of large knowledge graphs---labeled directed graphs---and predicting missing relationships---labeled edges. State-of-the-art embedding models propose different trade-offs between modeling expressiveness, and time and space complexity. We reconcile both expressiveness and complexity through the use of complex-valued embeddings and explore the link between such complex-valued embeddings and unitary diagonalization. We corroborate our approach theoretically and show that all real square matrices---thus all possible relation adjacency matrices---are the real part of some unitarily diagonalizable matrix. This results opens the door to a lot of other applications of square matrices factorization. Our approach based on complex embeddings is arguably simple, as it only involves a Hermitian dot product, the complex counterpart of the standard dot product between real vectors, whereas other methods resort to more and more complicated composition functions to increase their expressiveness. The proposed complex embeddings are scalable to large data sets as it remains linear in both space and time, while consistently outperforming alternative approaches on standard link prediction benchmarks.
Pairwise interaction models were also considered to improve prediction performances. For example, the Universal Schema approach @cite_34 factorizes a 2D unfolding of the tensor (a matrix of entity pairs vs. relations) while extend this also to other pairs. also consider augmenting the knowledge graph facts by exctracting them from textual data, as does . Injecting prior knowledge in the form of Horn clauses in the objective loss of the Universal Schema model has also been considered @cite_52 . enhance the RESCAL model to take into account information about the entity types. For recommender systems (thus with different subject object sets of entities), proposed a non-commutative extension of the CP decomposition model. More recently, Gaifman models that learn neighborhood embeddings of local structures in the knowledge graph showed competitive performances @cite_24 .
@cite_24 @cite_34 @cite_52
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Universal schema predicts the types of entities and relations in a knowledge base (KB) by jointly embedding the union of all available schema types---not only types from multiple structured databases (such as Freebase or Wikipedia infoboxes), but also types expressed as textual patterns from raw text. This prediction is typically modeled as a matrix completion problem, with one type per column, and either one or two entities per row (in the case of entity types or binary relation types, respectively). Factorizing this sparsely observed matrix yields a learned vector embedding for each row and each column. In this paper we explore the problem of making predictions for entities or entity-pairs unseen at training time (and hence without a pre-learned row embedding). We propose an approach having no per-row parameters at all; rather we produce a row vector on the fly using a learned aggregation function of the vectors of the observed columns for that row. We experiment with various aggregation functions, including neural network attention models. Our approach can be understood as a natural language database, in that questions about KB entities are answered by attending to textual or database evidence. In experiments predicting both relations and entity types, we demonstrate that despite having an order of magnitude fewer parameters than traditional universal schema, we can match the accuracy of the traditional model, and more importantly, we can now make predictions about unseen rows with nearly the same accuracy as rows available at training time. We consider learning representations of entities and relations in KBs using the neural-embedding approach. We show that most existing models, including NTN (, 2013) and TransE (, 2013b), can be generalized under a unified learning framework, where entities are low-dimensional vectors learned from a neural network and relations are bilinear and or linear mapping functions. Under this framework, we compare a variety of embedding models on the link prediction task. We show that a simple bilinear formulation achieves new state-of-the-art results for the task (achieving a top-10 accuracy of 73.2 vs. 54.7 by TransE on Freebase). Furthermore, we introduce a novel approach that utilizes the learned relation embeddings to mine logical rules such as "BornInCity(a,b) and CityInCountry(b,c) => Nationality(a,c)". We find that embeddings learned from the bilinear objective are particularly good at capturing relational semantics and that the composition of relations is characterized by matrix multiplication. More interestingly, we demonstrate that our embedding-based rule extraction approach successfully outperforms a state-of-the-art confidence-based rule mining approach in mining Horn rules that involve compositional reasoning. Universal schema builds a knowledge base (KB) of entities and relations by jointly embedding all relation types from input KBs as well as textual patterns expressing relations from raw text. In most previous applications of universal schema, each textual pattern is represented as a single embedding, preventing generalization to unseen patterns. Recent work employs a neural network to capture patterns' compositional semantics, providing generalization to all possible input text. In response, this paper introduces significant further improvements to the coverage and flexibility of universal schema relation extraction: predictions for entities unseen in training and multilingual transfer learning to domains with no annotation. We evaluate our model through extensive experiments on the English and Spanish TAC KBP benchmark, outperforming the top system from TAC 2013 slot-filling using no handwritten patterns or additional annotation. We also consider a multilingual setting in which English training data entities overlap with the seed KB, but Spanish text does not. Despite having no annotation for Spanish data, we train an accurate predictor, with additional improvements obtained by tying word embeddings across languages. Furthermore, we find that multilingual training improves English relation extraction accuracy. Our approach is thus suited to broad-coverage automated knowledge base construction in a variety of languages and domains. Knowledge graphs contain knowledge about the world and provide a structured representation of this knowledge. Current knowledge graphs contain only a small subset of what is true in the world. Link prediction approaches aim at predicting new links for a knowledge graph given the existing links between the entities. Tensor factorization approaches have proved promising for such link prediction problems. Proposed in 1927, Canonical Polyadic (CP) decomposition is among the first tensor factorization approaches. CP generally performs poorly for link prediction as it learns two independent embedding vectors for each entity, whereas they are really tied. We present a simple enhancement (which we call SimplE) of CP to allow the two embeddings of each entity to be learned dependently. The complexity of SimplE grows linearly with the size of embeddings. The embeddings learned through SimplE are interpretable, and certain types of background knowledge in terms of logical rules can be incorporated into these embeddings through weight tying. We prove SimplE is fully-expressive and derive a bound on the size of its embeddings for full expressivity. We show empirically that, despite its simplicity, SimplE outperforms several state-of-the-art tensor factorization techniques.