. Probabilistic inference algorithms for belief updating, finding the most probable explanation, the maximum a posteriori hypothesis, and the maximum expected utility are reformulated within the bucket elimination framework. This emphasizes the principles common to many of the algorithms appearing in the probabilistic inference literature and clarifies the relationship of such algorithms to nonserial dynamic programming algorithms. A general method for combining conditioning and bucket elimination is also presented. For all the algorithms, bounds on complexity are given as a function of the problem's structure. 1. Overview Bucket elimination is a unifying algorithmic framework that generalizes dynamic programming to accommodate algorithms for many complex problemsolving and reasoning activities, including directional resolution for propositional satisfiability (Davis and Putnam, 1960), adaptive consistency for constraint satisfaction (Dechter and Pearl, 1987), Fourier and Gaussian el...

Partially observable Markov decision processes (POMDPs) provide an elegant mathematical framework for modeling complex decision and planning problems in stochastic domains in which states of the system are observable only indirectly, via a set of imperfect or noisy observations. The modeling advantage of POMDPs, however, comes at a price — exact methods for solving them are computationally very expensive and thus applicable in practice only to very simple problems. We focus on efficient approximation (heuristic) methods that attempt to alleviate the computational problem and trade off accuracy for speed. We have two objectives here. First, we survey various approximation methods, analyze their properties and relations and provide some new insights into their differences. Second, we present a number of new approximation methods and novel refinements of existing techniques. The theoretical results are supported by experiments on a problem from the agent navigation domain. 1.

In this paper, we present a method for recognising an agent's behaviour in dynamic, noisy, uncertain domains, and across multiple levels of abstraction. We term this problem on-line plan recognition under uncertainty and view it generally as probabilistic inference on the stochastic process representing the execution of the agent's plan. Our contributions in this paper are twofold. In terms of probabilistic inference, we introduce the Abstract Hidden Markov Model (AHMM), a novel type of stochastic processes, provide its dynamic Bayesian network (DBN) structure and analyse the properties of this network. We then describe an application of the Rao-Blackwellised Particle Filter to the AHMM which allows us to construct an ecient, hybrid inference method for this model. In terms of plan recognition, we propose a novel plan recognition framework based on the AHMM as the plan execution model. The Rao-Blackwellised hybrid inference for AHMM can take advantage of the independence properties inherent in a model of plan execution, leading to an algorithm for online probabilistic plan recognition that scales well with the number of levels in the plan hierarchy. This illustrates that while stochastic models for plan execution can be complex, they exhibit special structures which, if exploited, can lead to efficient plan recognition algorithms. We demonstrate the usefulness of the AHMM framework via a behaviour recognition system in a complex spatial environment using distributed video surveillance data.

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The Factored Frontier (FF) algorithm is a simple approximate inference algorithm for Dynamic Bayesian Networks (DBNs). It is very similar to the fully factorized version of the Boyen-Koller (BK) algorithm, but instead of doing an exact update at every step followed by marginalisation (projection), it always works with factored distributions. Hence it can be applied to models for which the exact update step is intractable. We show that FF is equivalent to (one iteration of) loopy belief propagation (LBP) on the original DBN, and that BK is equivalent (to one iteration of) LBP on a DBN where we cluster some of the nodes. We then show empirically that by iterating more than once, LBP can improve on the accuracy of both FF and BK. We compare these algorithms on two real-world DBNs: the first is a model of a water treatment plant, and the second is a coupled HMM, used to model freeway trac.

In this paper, we consider the problem of tracking an object and predicting the object future trajectory in a wide-area environment, with complex spatial layout and the use of multiple sensors/cameras. To solve this problem, there is a need for representing the dynamic and noisy data in the tracking tasks, and dealing with them at different levels of detail. We employ the Abstract Hidden Markov Models (AHMM), an extension of the well-known Hidden Markov Model (HMM) and a special type of Dynamic Probabilistic Network (DPN), as our underlying representation framework. The AHMM allows us to explicitly encode the hierarchy of connected spatial locations, making it scalable to the size of the environment being modelled. We describe an application for tracking human movement in a...

We survey the literature on methods for inference and learning in Bayesian Networks composed of discrete and continuous nodes, in which the continuous nodes have a multivariate Gaussian distribution, whose mean and variance depends on the values of the discrete nodes. We also briefly consider hybrid Dynamic Bayesian Networks, an extension of switching Kalman filters. This report is meant to summarize what is known at a sufficient level of detail to enable someone to implement the algorithms, but without dwelling on formalities.

In recent years, there has been an increased need for the use of active systems- systems required to act automatically based on events, or changes in the environment. Such systems span many areas, from active databases to applications that drive the core business processes of today’s enterprises. However, in many cases, the events to which the system must respond are not generated by monitoring tools, but must be inferred from other events based on complex temporal predicates. In addition, in many applications, such inference is inherently uncertain. In this paper, we introduce a formal framework for knowledge representation and reasoning enabling such event inference. Based on probability theory, we de…ne the representation of the associated uncertainty. In addition, we formally de…ne the probability space, and show how the relevant probabilities can be calculated by dynamically constructing a Bayesian network. To the best of our knowledge, this is the …rst work that enables taking such uncertainty into account in the context of active systems. Therefore, our contribution is twofold: We formally de…ne the representation and semantics of event composition for probabilistic settings, and show how to apply these extensions to the quanti…cation of the occurrence probability of events. These results enable any active system to handle such uncertainty. 1