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.
Pairwise interaction models were also considered to improve prediction performances. For example, the Universal Schema approach @cite_15 factorizes a 2D unfolding of the tensor (a matrix of entity pairs vs. relations) while extend this also to other pairs.
@cite_15
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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. This paper contributes a joint embedding model for predicting relations between a pair of entities in the scenario of relation inference. It differs from most stand-alone approaches which separately operate on either knowledge bases or free texts. The proposed model simultaneously learns low-dimensional vector representations for both triplets in knowledge repositories and the mentions of relations in free texts, so that we can leverage the evidence both resources to make more accurate predictions. We use NELL to evaluate the performance of our approach, compared with cutting-edge methods. Results of extensive experiments show that our model achieves significant improvement on relation extraction. We propose a modular framework for multi-relational learning via tensor decomposition. In our learning setting, the training data contains multiple types of relationships among a set of objects, which we represent by a sparse three-mode tensor. The goal is to predict the values of the missing entries. To do so, we model each relationship as a function of a linear combination of latent factors. We learn this latent representation by computing a low-rank tensor decomposition, using quasi-Newton optimization of a weighted objective function. Sparsity in the observed data is captured by the weighted objective, leading to improved accuracy when training data is limited. Exploiting sparsity also improves efficiency, potentially up to an order of magnitude over unweighted approaches. In addition, our framework accommodates arbitrary combinations of smooth, task-specific loss functions, making it better suited for learning different types of relations. For the typical cases of real-valued functions and binary relations, we propose several loss functions and derive the associated parameter gradients. We evaluate our method on synthetic and real data, showing significant improvements in both accuracy and scalability over related factorization techniques. We model knowledge graphs for their completion by encoding each entity and relation into a numerical space. All previous work including Trans(E, H, R, and D) ignore the heterogeneity (some relations link many entity pairs and others do not) and the imbalance (the number of head entities and that of tail entities in a relation could be different) of knowledge graphs. In this paper, we propose a novel approach TranSparse to deal with the two issues. In TranSparse, transfer matrices are replaced by adaptive sparse matrices, whose sparse degrees are determined by the number of entities (or entity pairs) linked by relations. In experiments, we design structured and unstructured sparse patterns for transfer matrices and analyze their advantages and disadvantages. We evaluate our approach on triplet classification and link prediction tasks. Experimental results show that TranSparse outperforms Trans(E, H, R, and D) significantly, and achieves state-of-the-art performance.