Lifted Relax, Compensate and then Recover: From Approximate to Exact Lifted Probabilistic Inference

We propose an approach to lifted approximate inference for first-order probabilistic models, such as Markov logic networks. It is based on performing exact lifted inference in a simplified first-order model, which is found by relaxing first-order constraints, and then compensating for the relaxation. These simplified models can be incrementally improved by carefully recovering constraints that have been relaxed, also at the first-order level. This leads to a spectrum of approximations, with lifted belief propagation on one end, and exact lifted inference on the other. We discuss how relaxation, compensation, and recovery can be performed, all at the firstorder level, and show empirically that our approach substantially improves on the approximations of both propositional solvers and lifted belief propagation.Comment: Appears in Proceedings of the Twenty-Eighth Conference on Uncertainty in Artificial Intelligence (UAI2012

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

Coarse-to-Fine Lifted MAP Inference in Computer Vision

There is a vast body of theoretical research on lifted inference in probabilistic graphical models (PGMs). However, few demonstrations exist where lifting is applied in conjunction with top of the line applied algorithms. We pursue the applicability of lifted inference for computer vision (CV), with the insight that a globally optimal (MAP) labeling will likely have the same label for two symmetric pixels. The success of our approach lies in efficiently handling a distinct unary potential on every node (pixel), typical of CV applications. This allows us to lift the large class of algorithms that model a CV problem via PGM inference. We propose a generic template for coarse-to-fine (C2F) inference in CV, which progressively refines an initial coarsely lifted PGM for varying quality-time trade-offs. We demonstrate the performance of C2F inference by developing lifted versions of two near state-of-the-art CV algorithms for stereo vision and interactive image segmentation. We find that, against flat algorithms, the lifted versions have a much superior anytime performance, without any loss in final solution quality.Comment: Published in IJCAI 201

Accelerated Consensus via Min-Sum Splitting

We apply the Min-Sum message-passing protocol to solve the consensus problem in distributed optimization. We show that while the ordinary Min-Sum algorithm does not converge, a modified version of it known as Splitting yields convergence to the problem solution. We prove that a proper choice of the tuning parameters allows Min-Sum Splitting to yield subdiffusive accelerated convergence rates, matching the rates obtained by shift-register methods. The acceleration scheme embodied by Min-Sum Splitting for the consensus problem bears similarities with lifted Markov chains techniques and with multi-step first order methods in convex optimization