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303
Constraint Networks
, 1992
"... Constraintbased reasoning is a paradigm for formulating knowledge as a set of constraints without specifying the method by which these constraints are to be satisfied. A variety of techniques have been developed for finding partial or complete solutions for different kinds of constraint expression ..."
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Cited by 1149 (43 self)
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Constraintbased reasoning is a paradigm for formulating knowledge as a set of constraints without specifying the method by which these constraints are to be satisfied. A variety of techniques have been developed for finding partial or complete solutions for different kinds of constraint expressions. These have been successfully applied to diverse tasks such as design, diagnosis, truth maintenance, scheduling, spatiotemporal reasoning, logic programming and user interface. Constraint networks are graphical representations used to guide strategies for solving constraint satisfaction problems (CSPs).
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 758 (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.
The NPcompleteness column: an ongoing guide
 JOURNAL OF ALGORITHMS
, 1987
"... This is the nineteenth edition of a (usually) quarterly column that covers new developments in the theory of NPcompleteness. The presentation is modeled on that used by M. R. Garey and myself in our book "Computers and Intractability: A Guide to the Theory of NPCompleteness," W. H. Freem ..."
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Cited by 242 (0 self)
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This is the nineteenth edition of a (usually) quarterly column that covers new developments in the theory of NPcompleteness. The presentation is modeled on that used by M. R. Garey and myself in our book "Computers and Intractability: A Guide to the Theory of NPCompleteness," W. H. Freeman & Co., New York, 1979 (hereinafter referred to as "[G&J]"; previous columns will be referred to by their dates). A background equivalent to that provided by [G&J] is assumed, and, when appropriate, crossreferences will be given to that book and the list of problems (NPcomplete and harder) presented there. Readers who have results they would like mentioned (NPhardness, PSPACEhardness, polynomialtimesolvability, etc.) or open problems they would like publicized, should
Inference in belief networks: A procedural guide
 International Journal of Approximate Reasoning
, 1996
"... Belief networks are popular tools for encoding uncertainty in expert systems. These networks rely on inference algorithms to compute beliefs in the context of observed evidence. One established method for exact inference onbelief networks is the Probability Propagation in Trees of Clusters (PPTC) al ..."
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Cited by 179 (6 self)
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Belief networks are popular tools for encoding uncertainty in expert systems. These networks rely on inference algorithms to compute beliefs in the context of observed evidence. One established method for exact inference onbelief networks is the Probability Propagation in Trees of Clusters (PPTC) algorithm, as developed byLauritzen and Spiegelhalter and re ned by Jensen et al. [1, 2, 3] PPTC converts the belief network into a secondary structure, then computes probabilities by manipulating the secondary structure. In this document, we provide a selfcontained, procedural guide to understanding and implementing PPTC. We synthesize various optimizations to PPTC that are scattered throughout the literature. We articulate undocumented, \open secrets &quot; that are vital to producing a robust and e cient implementation of PPTC. We hope that this document makes probabilistic inference more accessible and a ordable to those without extensive prior exposure.
HYPERTREE DECOMPOSITIONS AND TRACTABLE QUERIES
, 1998
"... Several important decision problems on conjunctive queries (CQs) are NPcomplete in general but become tractable, and actually highly parallelizable, if restricted to acyclic or nearly acyclic queries. Examples are the evaluation of Boolean CQs and query containment. These problems were shown tracta ..."
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Cited by 166 (43 self)
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Several important decision problems on conjunctive queries (CQs) are NPcomplete in general but become tractable, and actually highly parallelizable, if restricted to acyclic or nearly acyclic queries. Examples are the evaluation of Boolean CQs and query containment. These problems were shown tractable for conjunctive queries of bounded treewidth [7], and of bounded degree of cyclicity [18, 17]. The so far most general concept of nearly acyclic queries was the notion of queries of bounded querywidth introduced by Chekuri and Rajaraman [7]. While CQs of bounded query width are tractable, it remained unclear whether such queries are efficiently recognizable. Chekuri and Rajaraman [7] stated as an open problem whether for each constant k it can be determined in polynomial time if a query has query width ≤ k. We give a negative answer by proving this problem NPcomplete (specifically, for k = 4). In order to circumvent this difficulty, we introduce the new concept of hypertree decomposition of a query and the corresponding notion of hypertree width. We prove: (a) for each k, the class of queries with query width bounded by k is properly contained in the class of queries whose hypertree width is bounded by k; (b) unlike query width, constant hypertreewidth is efficiently recognizable; (c) Boolean queries of constant hypertree width can be efficiently evaluated.
Multiresolution markov models for signal and image processing
 Proceedings of the IEEE
, 2002
"... This paper reviews a significant component of the rich field of statistical multiresolution (MR) modeling and processing. These MR methods have found application and permeated the literature of a widely scattered set of disciplines, and one of our principal objectives is to present a single, coheren ..."
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Cited by 154 (19 self)
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This paper reviews a significant component of the rich field of statistical multiresolution (MR) modeling and processing. These MR methods have found application and permeated the literature of a widely scattered set of disciplines, and one of our principal objectives is to present a single, coherent picture of this framework. A second goal is to describe how this topic fits into the even larger field of MR methods and concepts–in particular making ties to topics such as wavelets and multigrid methods. A third is to provide several alternate viewpoints for this body of work, as the methods and concepts we describe intersect with a number of other fields. The principle focus of our presentation is the class of MR Markov processes defined on pyramidally organized trees. The attractiveness of these models stems from both the very efficient algorithms they admit and their expressive power and broad applicability. We show how a variety of methods and models relate to this framework including models for selfsimilar and 1/f processes. We also illustrate how these methods have been used in practice. We discuss the construction of MR models on trees and show how questions that arise in this context make contact with wavelets, state space modeling of time series, system and parameter identification, and hidden
Conjunctive Query Containment Revisited
, 1998
"... We consider the problems of conjunctive query containment and minimization, which are known to be NPcomplete, and show that these problems can be solved in polynomial time for the class of acyclic queries. We then generalize the notion of acyclicity and define a parameter called query width that ca ..."
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Cited by 119 (0 self)
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We consider the problems of conjunctive query containment and minimization, which are known to be NPcomplete, and show that these problems can be solved in polynomial time for the class of acyclic queries. We then generalize the notion of acyclicity and define a parameter called query width that captures the "degree of cyclicity" of a query: in particular, a query is acyclic if and only if its query width is 1. We give algorithms for containment and minimization that run in time polynomial in n k , where n is the input size and k is the query width. These algorithms naturally generalize those for acyclic queries, and are of practical significance because many queries have small query width compared to their sizes. We show that good bounds on the query width of Q can be obtained using the treewidth of the incidence graph of Q. We then consider the problem of finding an equivalent query to a given conjunctive query Q that has the least number of subgoals. We show that a polynomial tim...
Decomposing Constraint Satisfaction Problems Using Database Techniques
, 1994
"... There is a very close relationship between constraint satisfaction problems and the satisfaction of joindependencies in a relational database which is due to a common underlying structure, namely a hypergraph. By making that relationship explicit we are able to adapt techniques previously developed ..."
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Cited by 95 (24 self)
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There is a very close relationship between constraint satisfaction problems and the satisfaction of joindependencies in a relational database which is due to a common underlying structure, namely a hypergraph. By making that relationship explicit we are able to adapt techniques previously developed for the study of relational databases to obtain new results for constraint satisfaction problems. In particular, we prove that a constraint satisfaction problem may be decomposed into a number of subproblems precisely when the corresponding hypergraph satisfies a simple condition. We show that combining this decomposition approach with existing algorithms can lead to a significant improvement in efficiency.
private communication
"... A rigid interval graph is an interval graph which has only one clique tree. In 2009, Panda and Das show that all connected unit interval graphs are rigid interval graphs. Generalizing the two classic graph search algorithms, Lexicographic BreadthFirst Search (LBFS) and Maximum Cardinality Search (M ..."
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Cited by 88 (6 self)
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A rigid interval graph is an interval graph which has only one clique tree. In 2009, Panda and Das show that all connected unit interval graphs are rigid interval graphs. Generalizing the two classic graph search algorithms, Lexicographic BreadthFirst Search (LBFS) and Maximum Cardinality Search (MCS), Corneil and Krueger propose in 2008 the socalled Maximal Neighborhood Search (MNS) and show that one sweep of MNS is enough to recognize chordal graphs. We develop the MNS properties of rigid interval graphs and characterize this graph class in several different ways. This allows us obtain several linear time multisweep MNS algorithms for recognizing rigid interval graphs and unit interval graphs, generalizing a corresponding 3sweep LBFS algorithm for unit interval graph recognition designed by Corneil in 2004. For unit interval graphs, we even present a new linear time 2sweep MNS certifying recognition algorithm. Submitted:
An Algorithm for Deciding if a Set of Observed Independencies Has a Causal Explanation
 Proc. of the Eighth Conference on Uncertainty in Artificial Intelligence
, 1992
"... In a previous paper [8] we presented an algorithm for extracting causal influences from independence information, where a causal influence was defined as the existence of a directed arc in all minimal causal models consistent with the data. In this paper we address the question of deciding whether t ..."
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Cited by 73 (2 self)
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In a previous paper [8] we presented an algorithm for extracting causal influences from independence information, where a causal influence was defined as the existence of a directed arc in all minimal causal models consistent with the data. In this paper we address the question of deciding whether there exists a causal model that explains ALL the observed dependencies and independencies. Formally, given a list M of conditional independence statements, it is required to decide whether there exists a directed acyclic graph D that is perfectly consistent with M, namely, every statement in M, and no other, is reflected via dseparation in D. We present and analyze an effective algorithm that tests for the existence of such a dag, and produces one, if it exists. Key words: Causal modeling, graphoids, conditional independence. 1 1 Introduction Directed acyclic graphs (dags) have been widely used for modeling statistical data. Starting with the pioneering work of Sewal Wright [...