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62
AND/OR Search Spaces for Graphical Models
, 2004
"... The paper introduces an AND/OR search space perspective for graphical models that include probabilistic networks (directed or undirected) and constraint networks. In contrast to the traditional (OR) search space view, the AND/OR search tree displays some of the independencies present in the gr ..."
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Cited by 119 (44 self)
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The paper introduces an AND/OR search space perspective for graphical models that include probabilistic networks (directed or undirected) and constraint networks. In contrast to the traditional (OR) search space view, the AND/OR search tree displays some of the independencies present in the graphical model explicitly and may sometime reduce the search space exponentially. Indeed, most
Compiling Bayesian Networks with Local Structure
"... Recent work on compiling Bayesian networks has reduced the problem to that of factoring CNF encodings of these networks, providing an expressive framework for exploiting local structure. For networks that have local structure, large CPTs, yet no excessive determinism, the quality of the CNF encoding ..."
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Cited by 51 (8 self)
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Recent work on compiling Bayesian networks has reduced the problem to that of factoring CNF encodings of these networks, providing an expressive framework for exploiting local structure. For networks that have local structure, large CPTs, yet no excessive determinism, the quality of the CNF encodings and the amount of local structure they capture can have a significant effect on both the offline compile time and online inference time. We examine the encoding of such Bayesian networks in this paper and report on new findings that allow us to significantly scale this compilation approach. In particular, we obtain order–of–magnitude improvements in compile time, compile some networks successfully for the first time, and obtain orders– of–magnitude improvements in online inference for some networks with local structure, as compared to baseline jointree inference, which does not exploit local structure.
Satisfiability Solvers
, 2008
"... The past few years have seen an enormous progress in the performance of Boolean satisfiability (SAT) solvers. Despite the worstcase exponential run time of all known algorithms, satisfiability solvers are increasingly leaving their mark as a generalpurpose tool in areas as diverse as software and h ..."
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Cited by 50 (0 self)
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The past few years have seen an enormous progress in the performance of Boolean satisfiability (SAT) solvers. Despite the worstcase exponential run time of all known algorithms, satisfiability solvers are increasingly leaving their mark as a generalpurpose tool in areas as diverse as software and hardware verification [29–31, 228], automatic test pattern generation [138, 221], planning [129, 197], scheduling [103], and even challenging problems from algebra [238]. Annual SAT competitions have led to the development of dozens of clever implementations of such solvers [e.g. 13,
On probabilistic inference by weighted model counting
 Artificial Intelligence
"... A recent and effective approach to probabilistic inference calls for reducing the problem to one of weighted model counting (WMC) on a propositional knowledge base. Specifically, the approach calls for encoding the probabilistic model, typically a Bayesian network, as a propositional knowledge base ..."
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Cited by 48 (5 self)
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A recent and effective approach to probabilistic inference calls for reducing the problem to one of weighted model counting (WMC) on a propositional knowledge base. Specifically, the approach calls for encoding the probabilistic model, typically a Bayesian network, as a propositional knowledge base in conjunctive normal form (CNF) with weights associated to each model according to the network parameters. Given this CNF, computing the probability of some evidence becomes a matter of summing the weights of all CNF models consistent with the evidence. A number of variations on this approach have appeared in the literature recently, that vary across three orthogonal dimensions. The first dimension concerns the specific encoding used to convert a Bayesian network into a CNF. The second dimensions relates to whether weighted model counting is performed using a search algorithm on the CNF, or by compiling the CNF into a structure that renders WMC a polytime operation in the size of the compiled structure. The third dimension deals with the specific properties of network parameters (local structure) which are captured in the CNF encoding. In this paper, we discuss recent work in this area across the above three dimensions, and demonstrate empirically its practical importance in significantly expanding the reach of exact probabilistic inference. We restrict our discussion to exact inference and model counting, even though other proposals have been extended for approximate inference and approximate model counting.
Value Elimination: Bayesian Inference via Backtracking Search
 IN UAI03
, 2003
"... We present Value Elimination, a new algorithm for Bayesian Inference. Given the same variable ordering information, Value Elimination can achieve performance that is within a constant factor of variable elimination or recursive conditioning, and on some problems it can perform exponentially bet ..."
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Cited by 43 (2 self)
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We present Value Elimination, a new algorithm for Bayesian Inference. Given the same variable ordering information, Value Elimination can achieve performance that is within a constant factor of variable elimination or recursive conditioning, and on some problems it can perform exponentially better, irrespective of the variable ordering used by these algorithms. Value Elimination
Performing bayesian inference by weighted model counting
 In Proceedings of the National Conference on Artificial Intelligence (AAAI
, 2005
"... Over the past decade general satisfiability testing algorithms have proven to be surprisingly effective at solving a wide variety of constraint satisfaction problem, such as planning and scheduling (Kautz and Selman 2003). Solving such NPcomplete tasks by “compilation to SAT ” has turned out to be a ..."
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Cited by 42 (0 self)
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Over the past decade general satisfiability testing algorithms have proven to be surprisingly effective at solving a wide variety of constraint satisfaction problem, such as planning and scheduling (Kautz and Selman 2003). Solving such NPcomplete tasks by “compilation to SAT ” has turned out to be an approach that is of both practical and theoretical interest. Recently, (Sang et al. 2004) have shown that state of the art SAT algorithms can be efficiently extended to the harder task of counting the number of models (satisfying assignments) of a formula, by employing a technique called component caching. This paper begins to investigate the question of whether “compilation to modelcounting ” could be a practical technique for solving realworld #Pcomplete problems, in particular Bayesian inference. We describe an efficient translation from Bayesian networks to weighted model counting, extend the best modelcounting algorithms to weighted model counting, develop an efficient method for computing all marginals in a single counting pass, and evaluate the approach on computationally challenging reasoning problems.
A Decision Network Framework for the Behavioral Animation of Virtual Humans
, 2007
"... We introduce a framework for advanced behavioral animation in virtual humans, which addresses the challenging open problem of simulating social interactions between pedestrians in urban settings. Based on hierarchical decision networks, our novel framework combines probability, decision, and graph t ..."
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Cited by 34 (2 self)
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We introduce a framework for advanced behavioral animation in virtual humans, which addresses the challenging open problem of simulating social interactions between pedestrians in urban settings. Based on hierarchical decision networks, our novel framework combines probability, decision, and graph theories for complex behavior modeling and intelligent action selection subject to manifold internal and external factors in the presence of uncertain knowledge. It yields autonomous characters that can make nontrivial interpretations and arrive at rational decisions dependent on multiple considerations. We demonstrate our framework in behavioral animation scenarios involving interacting autonomous pedestrians, including an elaborate emergency response animation. 1.
Fixedparameter algorithms for artificial intelligence, constraint satisfaction, and database problems
, 2007
"... We survey the parameterized complexity of problems that arise in artificial intelligence, database theory and automated reasoning. In particular, we consider various parameterizations of the constraint satisfaction problem, the evaluation problem of Boolean conjunctive database queries and the propo ..."
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Cited by 32 (10 self)
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We survey the parameterized complexity of problems that arise in artificial intelligence, database theory and automated reasoning. In particular, we consider various parameterizations of the constraint satisfaction problem, the evaluation problem of Boolean conjunctive database queries and the propositional satisfiability problem. Furthermore, we survey parameterized algorithms for problems arising in the context of the stable model semantics of logic programs, for a number of other problems of nonmonotonic reasoning, and for the computation of cores in data exchange.
Heuristics for fast exact model counting
 In Proc. 8th International Conference on Theory and Applications of Satisfiability Testing
, 2005
"... Abstract. An important extension of satisfiability testing is modelcounting, a task that corresponds to problems such as probabilistic reasoning and computing the permanent of a Boolean matrix. We recently introduced Cachet, an exact modelcounting algorithm that combines formula caching, clause le ..."
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Cited by 30 (2 self)
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Abstract. An important extension of satisfiability testing is modelcounting, a task that corresponds to problems such as probabilistic reasoning and computing the permanent of a Boolean matrix. We recently introduced Cachet, an exact modelcounting algorithm that combines formula caching, clause learning, and component analysis. This paper reports on experiments with various techniques for improving the performance of Cachet, including componentselection strategies, variableselection branching heuristics, randomization, backtracking schemes, and crosscomponent implications. The result of this work is a highlytuned version of Cachet, the first (and currently, only) system able to exactly determine the marginal probabilities of variables in random 3SAT formulas with 150+ variables. We use this to discover an interesting property of random formulas that does not seem to have been previously observed. 1
Algorithms for propositional model counting.
 In Proc. of the 14th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning (LPAR’07),
, 2007
"... Abstract We present algorithms for the propositional model counting problem #SAT. The algorithms utilize tree decompositions of certain graphs associated with the given CNF formula; in particular we consider primal, dual, and incidence graphs. We describe the algorithms coherently for a direct comp ..."
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Cited by 29 (10 self)
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Abstract We present algorithms for the propositional model counting problem #SAT. The algorithms utilize tree decompositions of certain graphs associated with the given CNF formula; in particular we consider primal, dual, and incidence graphs. We describe the algorithms coherently for a direct comparison and with sufficient detail for making an actual implementation reasonably easy. We discuss several aspects of the algorithms including worstcase time and space requirements.