Probabilistic (logic) programming concepts

A multitude of different probabilistic programming languages exists today, all extending a traditional programming language with primitives to support modeling of complex, structured probability distributions. Each of these languages employs its own probabilistic primitives, and comes with a particular syntax, semantics and inference procedure. This makes it hard to understand the underlying programming concepts and appreciate the differences between the different languages. To obtain a better understanding of probabilistic programming, we identify a number of core programming concepts underlying the primitives used by various probabilistic languages, discuss the execution mechanisms that they require and use these to position and survey state-of-the-art probabilistic languages and their implementation. While doing so, we focus on probabilistic extensions of logic programming languages such as Prolog, which have been considered for over 20 years

Graphical Models and Symmetries : Loopy Belief Propagation Approaches

Whenever a person or an automated system has to reason in uncertain domains, probability theory is necessary. Probabilistic graphical models allow us to build statistical models that capture complex dependencies between random variables. Inference in these models, however, can easily become intractable. Typical ways to address this scaling issue are inference by approximate message-passing, stochastic gradients, and MapReduce, among others. Exploiting the symmetries of graphical models, however, has not yet been considered for scaling statistical machine learning applications. One instance of graphical models that are inherently symmetric are statistical relational models. These have recently gained attraction within the machine learning and AI communities and combine probability theory with first-order logic, thereby allowing for an efficient representation of structured relational domains. The provided formalisms to compactly represent complex real-world domains enable us to effectively describe large problem instances. Inference within and training of graphical models, however, have not been able to keep pace with the increased representational power. This thesis tackles two major aspects of graphical models and shows that both inference and training can indeed benefit from exploiting symmetries. It first deals with efficient inference exploiting symmetries in graphical models for various query types. We introduce lifted loopy belief propagation (lifted LBP), the first lifted parallel inference approach for relational as well as propositional graphical models. Lifted LBP can effectively speed up marginal inference, but cannot straightforwardly be applied to other types of queries. Thus we also demonstrate efficient lifted algorithms for MAP inference and higher order marginals, as well as the efficient handling of multiple inference tasks. Then we turn to the training of graphical models and introduce the first lifted online training for relational models. Our training procedure and the MapReduce lifting for loopy belief propagation combine lifting with the traditional statistical approaches to scaling, thereby bridging the gap between statistical relational learning and traditional statistical machine learning

Lifted Bayesian filtering in multi-entity systems

This thesis focuses on Bayesian filtering for systems that consist of multiple, interacting entites (e.g. agents or objects), which can naturally be described by Multiset Rewriting Systems (MRSs). The main insight is that the state space that is underling an MRS exhibits a certain symmetry, which can be exploited to increase inference efficiency. We provide an efficient, lifted filtering algorithm, which is able to achieve a factorial reduction in space and time complexity, compared to conventional, ground filtering.Diese Arbeit betrachtet Bayes'sche Filter in Systemen, die aus mehreren, interagierenden Entitäten (z.B. Agenten oder Objekten) bestehen. Die Systemdynamik solcher Systeme kann auf natürliche Art durch Multiset Rewriting Systems (MRS) spezifiziert werden. Die wesentliche Erkenntnis ist, dass der Zustandraum Symmetrien aufweist, die ausgenutzt werden können, um die Effizienz der Inferenz zu erhöhen. Wir führen einen effizienten, gelifteten Filter-Algorithmus ein, dessen Zeit- und Platzkomplexität gegenüber dem grundierten Algorithmus um einen faktoriellen Faktor reduziert ist