The paper provides a unifying perspective of tree-decomposition algorithms appearing in various automated reasoning areas such as join-tree clustering for constraint-satisfaction and the clique-tree algorithm for probabilistic reasoning. Within this framework, we introduce a new algorithm, called bucket-tree elimination (BT E), that extends Bucket Elimination (BE) to trees, and show that it can provide a speed-up of n over BE for various reasoning tasks. Time-space tradeoffs of tree-decomposition processing are analyzed. 1

Recursive Conditioning (RC) was introduced recently as an any–space algorithm for inference in Bayesian networks which can trade time for space by varying the size of its cache at the increment needed to store a floating point number. Under full caching, RC has an asymptotic time and space complexity which is comparable to mainstream algorithms based on variable elimination and clustering (exponential in the network treewidth and linear in its size). We show two main results about RC in this paper. First, we show that its actual space requirements under full caching are much more modest than those needed by mainstream methods and study the implications of this finding. Second, we show that RC can effectively deal with determinism in Bayesian networks by employing standard logical techniques, such as unit resolution, allowing a significant reduction in its time requirements in certain cases. We illustrate our results using a number of benchmark networks, including the very challenging ones that arise in genetic linkage analysis. 1

We introduce a new generation of depth-first Branch-and-Bound algorithms that explore the AND/OR search tree using static and dynamic variable orderings for solving general constraint optimization problems. The virtue of the AND/OR representation of the search space is that its size may be far smaller than that of a traditional OR representation, which can translate into significant time savings for search algorithms. The focus of this paper is on linear space search which explores the AND/OR search tree rather than the search graph and therefore make no attempt to cache information. We investigate the power of the minibucket heuristics within the AND/OR search space, in both static and dynamic setups. We focus on two most common optimization problems in graphical models: finding the Most Probable Explanation (MPE) in Bayesian networks and solving Weighted CSPs (WCSP). In extensive empirical evaluations we demonstrate that the new AND/OR Branch-and-Bound approach improves considerably over the traditional OR search strategy and show how various variable ordering schemes impact the performance of the AND/OR search scheme.

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This paper describes a general framework called Hybrid Dynamic Mixed Networks (HDMNs) which are Hybrid Dynamic Bayesian Networks that allow representation of discrete deterministic information in the form of constraints. We propose approximate inference algorithms that integrate and adjust well known algorithmic principles such as Generalized Belief Propagation, Rao-Blackwellised Particle Filtering and Constraint Propagation to address the complexity of modeling and reasoning in HDMNs. We use this framework to model a person’s travel activity over time and to predict destination and routes given the current location. We present a preliminary empirical evaluation demonstrating the effectiveness of our modeling framework and algorithms using several variants of the activity model. 1

In this paper we explore the impact of caching on search in the context of the recent framework of AND/OR search in graphical models. Specifically, we extend the depth-first AND/OR Branch-and-Bound tree search algorithm to explore an AND/OR search graph by equipping it with an adaptive caching scheme similar to good and no-good recording. Furthermore, we present best-first search algorithms for traversing the same underlying AND/OR search graph and compare both depth-first and best-first approaches empirically. We focus on two common optimization problems in graphical models: finding the Most Probable Explanation (MPE) in belief networks and solving Weighted CSPs (WCSP). In an extensive empirical evaluation we demonstrate conclusively the superiority of the memory intensive AND/OR search algorithms on a variety of benchmarks including random and real-world problem instances.

The paper focuses on developing effective importance sampling algorithms for mixed probabilistic and deterministic graphical models. The use of importance sampling in such graphical models is problematic because it generates many useless zero weight samples which are rejected yielding an inefficient sampling process. To address this rejection problem, we propose the SampleSearch scheme that augments sampling with systematic constraint-based backtracking search. We characterize the bias introduced by the combination of search with sampling, and derive a weighting scheme which yields an unbiased estimate of the desired statistics (e.g. probability of evidence). When computing the weights exactly is too complex, we propose an approximation which has a weaker guarantee of asymptotic unbiasedness. We present results of an extensive empirical evaluation demonstrating that SampleSearch outperforms other schemes in presence of significant amount of determinism.

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Numerous temporal inference tasks such as fault monitoring and anomaly detection exhibit a persistence property: for example, if something breaks, it stays broken until an intervention. When modeled as a Dynamic Bayesian Network, persistence adds dependencies between adjacent time slices, often making exact inference over time intractable using standard inference algorithms. However, we show that persistence implies a regular structure that can be exploited for efficient inference. We present three successively more general classes of models: persistent causal chains (PCCs), persistent causal trees (PCTs) and persistent polytrees (PPTs), and the corresponding exact inference algorithms that exploit persistence. We show that analytic asymptotic bounds for our algorithms compare favorably to junction tree inference; and we demonstrate empirically that we can perform exact smoothing on the order of 100 times faster than the approximate Boyen-Koller method on randomly generated instances of persistent tree models. We also show how to handle non-persistent variables and how persistence can be exploited effectively for approximate filtering. 1