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111
Dynamic Bayesian Networks: Representation, Inference and Learning
, 2002
"... Modelling sequential data is important in many areas of science and engineering. Hidden Markov models (HMMs) and Kalman filter models (KFMs) are popular for this because they are simple and flexible. For example, HMMs have been used for speech recognition and biosequence analysis, and KFMs have bee ..."
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Cited by 564 (3 self)
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Modelling sequential data is important in many areas of science and engineering. Hidden Markov models (HMMs) and Kalman filter models (KFMs) are popular for this because they are simple and flexible. For example, HMMs have been used for speech recognition and biosequence analysis, and KFMs have been used for problems ranging from tracking planes and missiles to predicting the economy. However, HMMs
and KFMs are limited in their “expressive power”. Dynamic Bayesian Networks (DBNs) generalize HMMs by allowing the state space to be represented in factored form, instead of as a single discrete random variable. DBNs generalize KFMs by allowing arbitrary probability distributions, not just (unimodal) linearGaussian. In this thesis, I will discuss how to represent many different kinds of models as DBNs, how to perform exact and approximate inference in DBNs, and how to learn DBN models from sequential data.
In particular, the main novel technical contributions of this thesis are as follows: a way of representing
Hierarchical HMMs as DBNs, which enables inference to be done in O(T) time instead of O(T 3), where T is the length of the sequence; an exact smoothing algorithm that takes O(log T) space instead of O(T); a simple way of using the junction tree algorithm for online inference in DBNs; new complexity bounds on exact online inference in DBNs; a new deterministic approximate inference algorithm called factored frontier; an analysis of the relationship between the BK algorithm and loopy belief propagation; a way of
applying RaoBlackwellised particle filtering to DBNs in general, and the SLAM (simultaneous localization
and mapping) problem in particular; a way of extending the structural EM algorithm to DBNs; and a variety of different applications of DBNs. However, perhaps the main value of the thesis is its catholic presentation of the field of sequential data modelling.
Pure Nash Equilibria: Hard and Easy Games
"... In this paper we investigate complexity issues related to pure Nash equilibria of strategic games. We show that, even in very restrictive settings, determining whether a game has a pure Nash Equilibrium is NPhard, while deciding whether a game has a strong Nash equilibrium is Stcomplete. We then s ..."
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Cited by 63 (2 self)
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In this paper we investigate complexity issues related to pure Nash equilibria of strategic games. We show that, even in very restrictive settings, determining whether a game has a pure Nash Equilibrium is NPhard, while deciding whether a game has a strong Nash equilibrium is Stcomplete. We then study practically relevant restrictions that lower the complexity. In particular, we are interested in quantitative and qualitative restrictions of the way each player's move depends on moves of other players. We say that a game has small neighborhood if the " utility function for each player depends only on (the actions of) a logarithmically small number of other players, The dependency structure of a game G can he expressed by a graph G(G) or by a hypergraph II(G). Among other results, we show that if jC has small neighborhood and if II(G) has botmdecl hypertree width (or if G(G) has bounded treewidth), then finding pure Nash and Pareto equilibria is feasible in polynomial time. If the game is graphical, then these problems are LOGCFLcomplete and thus in the class _NC ~ of highly parallelizable problems. 1 Introduction and Overview of Results The theory of strategic games and Nash equilibria has important applications in economics and decision making [31, 2]. Determining whether Nash equilibria exist, and effectively computing
Iterative JoinGraph Propagation
 IN UAI ’02
, 2002
"... The paper presents an iterative version of jointree clustering that applies the message passing of jointree clustering algorithm to joingraphs rather than to jointrees, iteratively. ..."
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Cited by 56 (19 self)
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The paper presents an iterative version of jointree clustering that applies the message passing of jointree clustering algorithm to joingraphs rather than to jointrees, iteratively.
PartitionBased Logical Reasoning for FirstOrder and Propositional Theories
 Artificial Intelligence
, 2000
"... In this paper we provide algorithms for reasoning with partitions of related logical axioms in propositional and firstorder logic (FOL). We also provide a greedy algorithm that automatically decomposes a set of logical axioms into partitions. Our motivation is twofold. First, we are concerned with ..."
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Cited by 52 (8 self)
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In this paper we provide algorithms for reasoning with partitions of related logical axioms in propositional and firstorder logic (FOL). We also provide a greedy algorithm that automatically decomposes a set of logical axioms into partitions. Our motivation is twofold. First, we are concerned with how to reason e#ectively with multiple knowledge bases that have overlap in content. Second, we are concerned with improving the e#ciency of reasoning over a set of logical axioms by partitioning the set with respect to some detectable structure, and reasoning over individual partitions. Many of the reasoning procedures we present are based on the idea of passing messages between partitions. We present algorithms for reasoning using forward messagepassing and using backward messagepassing with partitions of logical axioms. Associated with each partition is a reasoning procedure. We characterize a class of reasoning procedures that ensures completeness and soundness of our messagepassing ...
Hybrid backtracking bounded by treedecomposition of constraint networks
 Artificial Intelligence
, 2003
"... We propose a framework for solving CSPs based both on backtracking techniques and on the notion of treedecomposition of the constraint networks. This mixed approach permits us to define a new framework for the enumeration, which we expect that it will benefit from the advantages of two approaches: ..."
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Cited by 51 (16 self)
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We propose a framework for solving CSPs based both on backtracking techniques and on the notion of treedecomposition of the constraint networks. This mixed approach permits us to define a new framework for the enumeration, which we expect that it will benefit from the advantages of two approaches: a practical efficiency of enumerative algorithms and a warranty of a limited time complexity by an approximation of the treewidth of the constraint networks. Finally, experimental results allow us to show the advantages of this approach. 1
Backjumpbased techniques versus conflictdirected heuristics
 In Proceedings of ICTAI’04
, 2004
"... In this paper, we present a general algorithm which gives an uniform view of several stateoftheart systematic backtracking search algorithms for solving both binary and nonbinary CSP instances. More precisely, this algorithm integrates the most usual or/and sophisticated lookback and lookahead ..."
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Cited by 30 (11 self)
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In this paper, we present a general algorithm which gives an uniform view of several stateoftheart systematic backtracking search algorithms for solving both binary and nonbinary CSP instances. More precisely, this algorithm integrates the most usual or/and sophisticated lookback and lookahead schemes. By means of this algorithm, our purpose is then to study the interest of backjumpbased techniques with respect to conflictdirected variable ordering heuristics. 1
Hypertree decompositions: A survey
 In: MFCS ’01: Proceedings of the 26th International Symposium on Mathematical Foundations of Computer Science
, 2001
"... Abstract. This paper surveys recent results related to the concept of hypertree decomposition and the associated notion of hypertree width. A hypertree decomposition of a hypergraph (similar to a tree decomposition of a graph) is a suitable clustering of its hyperedges yielding a tree or a forest. I ..."
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Cited by 29 (4 self)
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Abstract. This paper surveys recent results related to the concept of hypertree decomposition and the associated notion of hypertree width. A hypertree decomposition of a hypergraph (similar to a tree decomposition of a graph) is a suitable clustering of its hyperedges yielding a tree or a forest. Important NP hard problems become tractable if restricted to instances whose associated hypergraphs are of bounded hypertree width. We also review a number of complexity results on problems whose structure is described by acyclic or nearly acyclic hypergraphs. 1
A General Scheme for Multiple Lower Bound Computation in Constraint Optimization
 In Constraint Programming
, 2001
"... . Computing lower bounds to the bestcost extension of a tuple is an ubiquous task in constraint optimization. A particular case of special interest is the computation of lower bounds to all singleton tuples, since it permits domain pruning in Branch and Bound algorithms. In this paper we introd ..."
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Cited by 28 (11 self)
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. Computing lower bounds to the bestcost extension of a tuple is an ubiquous task in constraint optimization. A particular case of special interest is the computation of lower bounds to all singleton tuples, since it permits domain pruning in Branch and Bound algorithms. In this paper we introduce MCTE(z), a general algorithm which allows the computation of lower bounds to arbitrary sets of tasks. Its time and accuracy grows as a function of z allowing a controlled tradeoff between lower bound accuracy and time and space to fit available resources. Subsequently, a specialization of MCTE(z) called MBTE(z) is tailored to computing lower bounds to singleton tuples. Preliminary experiments on MaxCSP show that using MBTE(z) to guide dynamic variable and value orderings in branch and bound yields a dramatic reduction in the search space and, for some classes of problems, this reduction is highly costeffective producing significant time savings and is competative against specialized algorithms for MaxCSP. 1
Bounded backtracking for the valued constraint satisfaction problems
 Proc. CP03 (2003
, 2003
"... Abstract. We propose a new method for solving Valued Constraint Satisfaction Problems based both on backtracking techniques branch and bound and the notion of treedecomposition of valued constraint networks. This mixed method aims to benefit from the practical efficiency of enumerative algorithms ..."
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Cited by 23 (7 self)
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Abstract. We propose a new method for solving Valued Constraint Satisfaction Problems based both on backtracking techniques branch and bound and the notion of treedecomposition of valued constraint networks. This mixed method aims to benefit from the practical efficiency of enumerative algorithms while providing a warranty of a bounded time complexity. Indeed the time complexity of our method is O(d w+ +1) with w + an approximation of the treewidth of the constraint network and d the maximum size of domains. Such a complexity is obtained by exploiting optimal bounds on the subproblems defined from the treedecomposition. These bounds associated to some partial assignments are called ”structural valued goods”. Recording and exploiting these goods may allow our method to save some time and space with respect to ones required by classical dynamic programming methods. Finally, this method is a natural extension of the BTD algorithm [1] proposed in the classical CSP framework. 1
A unified theory of structural tractability for constraint satisfaction and spread cut decomposition
 In Proceedings of the 19th International Joint Conference on Artificial Intelligence
, 2005
"... In this paper we introduce a generic form of structural decomposition for the constraint satisfaction problem, which we call a guarded decomposition. We show that many existing decomposition methods can be characterized in terms of finding guarded decompositions satisfying certain specified addition ..."
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Cited by 21 (2 self)
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In this paper we introduce a generic form of structural decomposition for the constraint satisfaction problem, which we call a guarded decomposition. We show that many existing decomposition methods can be characterized in terms of finding guarded decompositions satisfying certain specified additional conditions. Using the guarded decomposition framework we are also able to define a new form of decomposition, which we call a spread cut. We show that discovery of width k spreadcut decompositions is tractable for each k, and that the spread cut decomposition strongly generalize all existing decompositions except hypertrees. Finally we exhibit a family of hypergraphs Hn, for n = 1, 2, 3..., where the width of the best hypertree decomposition of each Hn is at least 3n, but the width of the best spreadcut decomposition is at most 2n. 1