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Krompaß, Denis (2015): Exploiting prior knowledge and latent variable representations for the statistical modeling and probabilistic querying of large knowledge graphs. Dissertation, LMU München: Fakultät für Mathematik, Informatik und Statistik



Large knowledge graphs increasingly add great value to various applications that require machines to recognize and understand queries and their semantics, as in search or question answering systems. These applications include Google search, Bing search, IBM’s Watson, but also smart mobile assistants as Apple’s Siri, Google Now or Microsoft’s Cortana. Popular knowledge graphs like DBpedia, YAGO or Freebase store a broad range of facts about the world, to a large extent derived from Wikipedia, currently the biggest web encyclopedia. In addition to these freely accessible open knowledge graphs, commercial ones have also evolved including the well-known Google Knowledge Graph or Microsoft’s Satori. Since incompleteness and veracity of knowledge graphs are known problems, the statistical modeling of knowledge graphs has increasingly gained attention in recent years. Some of the leading approaches are based on latent variable models which show both excellent predictive performance and scalability. Latent variable models learn embedding representations of domain entities and relations (representation learning). From these embeddings, priors for every possible fact in the knowledge graph are generated which can be exploited for data cleansing, completion or as prior knowledge to support triple extraction from unstructured textual data as successfully demonstrated by Google’s Knowledge-Vault project. However, large knowledge graphs impose constraints on the complexity of the latent embeddings learned by these models. For graphs with millions of entities and thousands of relation-types, latent variable models are required to exploit low dimensional embeddings for entities and relation-types to be tractable when applied to these graphs. The work described in this thesis extends the application of latent variable models for large knowledge graphs in three important dimensions. First, it is shown how the integration of ontological constraints on the domain and range of relation-types enables latent variable models to exploit latent embeddings of reduced complexity for modeling large knowledge graphs. The integration of this prior knowledge into the models leads to a substantial increase both in predictive performance and scalability with improvements of up to 77% in link-prediction tasks. Since manually designed domain and range constraints can be absent or fuzzy, we also propose and study an alternative approach based on a local closed-world assumption, which derives domain and range constraints from observed data without the need of prior knowledge extracted from the curated schema of the knowledge graph. We show that such an approach also leads to similar significant improvements in modeling quality. Further, we demonstrate that these two types of domain and range constraints are of general value to latent variable models by integrating and evaluating them on the current state of the art of latent variable models represented by RESCAL, Translational Embedding, and the neural network approach used by the recently proposed Google Knowledge Vault system. In the second part of the thesis it is shown that the just mentioned three approaches all perform well, but do not share many commonalities in the way they model knowledge graphs. These differences can be exploited in ensemble solutions which improve the predictive performance even further. The third part of the thesis concerns the efficient querying of the statistically modeled knowledge graphs. This thesis interprets statistically modeled knowledge graphs as probabilistic databases, where the latent variable models define a probability distribution for triples. From this perspective, link-prediction is equivalent to querying ground triples which is a standard functionality of the latent variable models. For more complex querying that involves e.g. joins and projections, the theory on probabilistic databases provides evaluation rules. In this thesis it is shown how the intrinsic features of latent variable models can be combined with the theory of probabilistic databases to realize efficient probabilistic querying of the modeled graphs.