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.
 Over the last few years, RDF has been used as a knowledge representation model in a wide variety of domains. Some domains are full of uncertainty. Thus, it is desired to process and manage probabilistic RDF data. The core operation of queries on an RDF probabilistic database is computing the probability of the result to a query. In this paper, we describe a general framework for supporting SPARQL queries on probabilistic RDF databases. In particular, we consider transitive inference capability for RDF instance data. We show that the find operation for an atomic query with the transitive property can be formalized as the problem of computing path expressions on the transitive relation graph and we also propose an approximate algorithm for computing path expressions efficiently. At last, we implement and experimentally evaluate our approach. DBpedia is a community effort to extract structured information from Wikipedia and to make this information available on the Web. DBpedia allows you to ask sophisticated queries against datasets derived from Wikipedia and to link other datasets on the Web to Wikipedia data. We describe the extraction of the DBpedia datasets, and how the resulting information is published on the Web for human-andmachine-consumption. We describe some emerging applications from the DBpedia community and show how website authors can facilitate DBpedia content within their sites. Finally, we present the current status of interlinking DBpedia with other open datasets on the Web and outline how DBpedia could serve as a nucleus for an emerging Web of open data. Freebase is a practical, scalable tuple database used to structure general human knowledge. The data in Freebase is collaboratively created, structured, and maintained. Freebase currently contains more than 125,000,000 tuples, more than 4000 types, and more than 7000 properties. Public read write access to Freebase is allowed through an HTTP-based graph-query API using the Metaweb Query Language (MQL) as a data query and manipulation language. MQL provides an easy-to-use object-oriented interface to the tuple data in Freebase and is designed to facilitate the creation of collaborative, Web-based data-oriented applications. An increasing amount of data is becoming available in the form of large triple stores, with the Semantic Web's linked open data cloud (LOD) as one of the most prominent examples. Data quality and completeness are key issues in many community-generated data stores, like LOD, which motivates probabilistic and statistical approaches to data representation, reasoning and querying. In this paper we address the issue from the perspective of probabilistic databases, which account for uncertainty in the data via a probability distribution over all database instances. We obtain a highly compressed representation using the recently developed RESCAL approach and demonstrate experimentally that efficient querying can be obtained by exploiting inherent features of RESCAL via sub-query approximations of deterministic views. Building computers able to answer questions on any subject is a long standing goal of artificial intelligence. Promising progress has recently been achieved by methods that learn to map questions to logical forms or database queries. Such approaches can be effective but at the cost of either large amounts of human-labeled data or by defining lexicons and grammars tailored by practitioners. In this paper, we instead take the radical approach of learning to map questions to vectorial feature representations. By mapping answers into the same space one can query any knowledge base independent of its schema, without requiring any grammar or lexicon. Our method is trained with a new optimization procedure combining stochastic gradient descent followed by a fine-tuning step using the weak supervision provided by blending automatically and collaboratively generated resources. We empirically demonstrate that our model can capture meaningful signals from its noisy supervision leading to major improvements over paralex, the only existing method able to be trained on similar weakly labeled data. Recent years have witnessed a proliferation of large-scale knowledge bases, including Wikipedia, Freebase, YAGO, Microsoft's Satori, and Google's Knowledge Graph. To increase the scale even further, we need to explore automatic methods for constructing knowledge bases. Previous approaches have primarily focused on text-based extraction, which can be very noisy. Here we introduce Knowledge Vault, a Web-scale probabilistic knowledge base that combines extractions from Web content (obtained via analysis of text, tabular data, page structure, and human annotations) with prior knowledge derived from existing knowledge repositories. We employ supervised machine learning methods for fusing these distinct information sources. The Knowledge Vault is substantially bigger than any previously published structured knowledge repository, and features a probabilistic inference system that computes calibrated probabilities of fact correctness. We report the results of multiple studies that explore the relative utility of the different information sources and extraction methods.