Lifted graphical models: a survey

Lifted graphical models provide a language for expressing dependencies between different types of entities, their attributes, and their diverse relations, as well as techniques for probabilistic reasoning in such multi-relational domains. In this survey, we review a general form for a lifted graphical model, a par-factor graph, and show how a number of existing statistical relational representations map to this formalism. We discuss inference algorithms, including lifted inference algorithms, that efficiently compute the answers to probabilistic queries over such models. We also review work in learning lifted graphical models from data. There is a growing need for statistical relational models (whether they go by that name or another), as we are inundated with data which is a mix of structured and unstructured, with entities and relations extracted in a noisy manner from text, and with the need to reason effectively with this data. We hope that this synthesis of ideas from many different research groups will provide an accessible starting point for new researchers in this expanding field

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

Architectures and GPU-Based Parallelization for Online Bayesian Computational Statistics and Dynamic Modeling

Recent work demonstrates that coupling Bayesian computational statistics methods with dynamic models can facilitate the analysis of complex systems associated with diverse time series, including those involving social and behavioural dynamics. Particle Markov Chain Monte Carlo (PMCMC) methods constitute a particularly powerful class of Bayesian methods combining aspects of batch Markov Chain Monte Carlo (MCMC) and the sequential Monte Carlo method of Particle Filtering (PF). PMCMC can flexibly combine theory-capturing dynamic models with diverse empirical data. Online machine learning is a subcategory of machine learning algorithms characterized by sequential, incremental execution as new data arrives, which can give updated results and predictions with growing sequences of available incoming data. While many machine learning and statistical methods are adapted to online algorithms, PMCMC is one example of the many methods whose compatibility with and adaption to online learning remains unclear. In this thesis, I proposed a data-streaming solution supporting PF and PMCMC methods with dynamic epidemiological models and demonstrated several successful applications. By constructing an automated, easy-to-use streaming system, analytic applications and simulation models gain access to arriving real-time data to shorten the time gap between data and resulting model-supported insight. The well-defined architecture design emerging from the thesis would substantially expand traditional simulation models' potential by allowing such models to be offered as continually updated services. Contingent on sufficiently fast execution time, simulation models within this framework can consume the incoming empirical data in real-time and generate informative predictions on an ongoing basis as new data points arrive. In a second line of work, I investigated the platform's flexibility and capability by extending this system to support the use of a powerful class of PMCMC algorithms with dynamic models while ameliorating such algorithms' traditionally stiff performance limitations. Specifically, this work designed and implemented a GPU-enabled parallel version of a PMCMC method with dynamic simulation models. The resulting codebase readily has enabled researchers to adapt their models to the state-of-art statistical inference methods, and ensure that the computation-heavy PMCMC method can perform significant sampling between the successive arrival of each new data point. Investigating this method's impact with several realistic PMCMC application examples showed that GPU-based acceleration allows for up to 160x speedup compared to a corresponding CPU-based version not exploiting parallelism. The GPU accelerated PMCMC and the streaming processing system can complement each other, jointly providing researchers with a powerful toolset to greatly accelerate learning and securing additional insight from the high-velocity data increasingly prevalent within social and behavioural spheres. The design philosophy applied supported a platform with broad generalizability and potential for ready future extensions. The thesis discusses common barriers and difficulties in designing and implementing such systems and offers solutions to solve or mitigate them