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

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

On Leveraging Statistical and Relational Information for the Representation and Recognition of Complex Human Activities

Machine activity recognition aims to automatically predict human activities from a series of sensor signals. It is a key aspect to several emerging applications, especially in the pervasive computing field. However, this problem faces several challenges due to the complex, relational and ambiguous nature of human activities. These challenges still defy the majority of traditional pattern recognition approaches, whether they are knowledge-based or data-driven. Concretely, the current approaches to activity recognition in sensor environments fall short to represent, reason or learn under uncertainty, complex relational structure, rich temporal context and abundant common-sense knowledge. Motivated by these shortcomings, our work focuses on the combination of both data-driven and knowledge-based paradigms in order to address this problem. In particular, we propose two logic-based statistical relational activity recognition frameworks which we describe in two different parts. The first part presents a Markov logic-based framework addressing the recognition of complex human activities under realistic settings. Markov logic is a highly flexible statistical relational formalism combining the power of first-order logic with Markov networks by attaching real-valued weights to formulas in first-order logic. Thus, it unites both symbolic and probabilistic reasoning and allows to model the complex relational structure as well as the inherent uncertainty underlying human activities and sensor data. We focus on addressing the challenge of recognizing interleaved and concurrent activities while preserving the intuitiveness and flexibility of the modelling task. Using three different models we evaluate and prove the viability of using Markov logic networks for that problem statement. We also demonstrate the crucial impact of domain knowledge on the recognition outcome. Implementing an exhaustive model including heterogeneous information sources comes, however, at considerable knowledge engineering efforts. Hence, employing a standard, widely used formalism can alleviate that by enhancing the portability, the re-usability and the extension of the model. In the second part of this document, we apply a hybrid approach that goes one step further than Markov logic network towards a formal, yet intuitive conceptualization of the domain of discourse. Concretely, we propose an activity recognition framework based on log-linear description logic, a probabilistic variant of description logics. Log-linear description logic leverages the principles of Markov logic while allowing for a formal conceptualization of the domain of discourse, backed up with powerful reasoning and consistency check tools. Based on principles from the activity theory, we focus on addressing the challenge of representing and recognizing human activities at three levels of granularity: operations, actions and activities. Complying with real-life scenarios, we assess and discuss the viability of the proposed framework. In particular, we show the positive impact of augmenting the proposed multi-level activity ontology with weights compared to using its conventional weight-free variant