Efficient Maximum A-Posteriori Inference in Markov Logic and Application in Description Logics

Noessner, Jan

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URL: https://ub-madoc.bib.uni-mannheim.de/36586
URN: urn:nbn:de:bsz:180-madoc-365866
Document Type: Doctoral dissertation
Year of publication: 2014
Place of publication: Mannheim
University: Universität Mannheim
Evaluator: Stuckenschmidt, Heiner
Date of oral examination: 19 May 2014
Publication language: English
Institution: School of Business Informatics and Mathematics > Praktische Informatik II (Stuckenschmidt 2009-)
Subject: 004 Computer science, internet
Subject headings (SWD): Log-lineares Modell , Aggregation , Schlussfolgern , Ontologie , Symmetrie
Keywords (English): Markov Logic , Maximum A-Posteriori Inference , symmetry detection , lifted inference , cutting plane aggregation , counting constraint , log-linear models , log-linear description logics , most probable coherent ontology , data integration
Abstract: Maximum a-posteriori (MAP) query in statistical relational models computes the most probable world given evidence and further knowledge about the domain. It is arguably one of the most important types of computational problems, since it is also used as a subroutine in weight learning algorithms. In this thesis, we discuss an improved inference algorithm and an application for MAP queries. We focus on Markov logic (ML) as statistical relational formalism. Markov logic combines Markov networks with first-order logic by attaching weights to first-order formulas. For inference, we improve existing work which translates MAP queries to integer linear programs (ILP). The motivation is that existing ILP solvers are very stable and fast and are able to precisely estimate the quality of an intermediate solution. In our work, we focus on improving the translation process such that we result in ILPs having fewer variables and fewer constraints. Our main contribution is the Cutting Plane Aggregation (CPA) approach which leverages symmetries in ML networks and parallelizes MAP inference. Additionally, we integrate the cutting plane inference (Riedel 2008) algorithm which significantly reduces the number of groundings by solving multiple smaller ILPs instead of one large ILP. We present the new Markov logic engine RockIt which outperforms state-of-the-art engines in standard Markov logic benchmarks. Afterwards, we apply the MAP query to description logics. Description logics (DL) are knowledge representation formalisms whose expressivity is higher than propositional logic but lower than first-order logic. The most popular DLs have been standardized in the ontology language OWL and are an elementary component in the Semantic Web. We combine Markov logic, which essentially follows the semantic of a log-linear model, with description logics to log-linear description logics. In log-linear description logic weights can be attached to any description logic axiom. Furthermore, we introduce a new query type which computes the most-probable 'coherent' world. Possible applications of log-linear description logics are mainly located in the area of ontology learning and data integration. With our novel log-linear description logic reasoner ELog, we experimentally show that more expressivity increases quality and that the solutions of optimal solving strategies have higher quality than the solutions of approximate solving strategies.

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