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Axioms for probability and belieffunction propagation
 Uncertainty in Artificial Intelligence
, 1990
"... In this paper, we describe an abstract framework and axioms under which exact local computation of marginals is possible. The primitive objects of the framework are variables and valuations. The primitive operators of the framework are combination and marginalization. These operate on valuations. We ..."
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Cited by 137 (17 self)
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In this paper, we describe an abstract framework and axioms under which exact local computation of marginals is possible. The primitive objects of the framework are variables and valuations. The primitive operators of the framework are combination and marginalization. These operate on valuations. We state three axioms for these operators and we derive the possibility of local computation from the axioms. Next, we describe a propagation scheme for computing marginals of a valuation when we have a factorization of the valuation on a hypertree. Finally we show how the problem of computing marginals of joint probability distributions and joint belief functions fits the general framework. 1.
An efficient algorithm for finding the M most probable configurations in probabilistic expert systems
 Statistics and Computing
, 1998
"... A probabilistic expert system provides a graphical representation of a joint probability distribution which enables local computations of probabilities. Dawid (1992) provided a `flowpropagation' algorithm for finding the most probable configuration of the joint distribution in such a system. This p ..."
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Cited by 68 (3 self)
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A probabilistic expert system provides a graphical representation of a joint probability distribution which enables local computations of probabilities. Dawid (1992) provided a `flowpropagation' algorithm for finding the most probable configuration of the joint distribution in such a system. This paper analyses that algorithm in detail, and shows how it can be combined with a clever partitioning scheme to formulate an efficient method for finding the M most probable configurations. The algorithm is a divide and conquer technique, that iteratively identifies the M most probable configurations. The algorithm has been implemented into the experimental shell XBAIES, which is an extension of BAIES (Cowell, 1992). Keywords: Bayesian network, belief revision, most probable explanation, junction tree, maximization, propagation, charge, potential function, conditional independence, flow, evidence, marginalization, divideandconquer. 1 Introduction A probabilistic expert system (PES) funct...
An Alternative Markov Property for Chain Graphs
 Scand. J. Statist
, 1996
"... Graphical Markov models use graphs, either undirected, directed, or mixed, to represent possible dependences among statistical variables. Applications of undirected graphs (UDGs) include models for spatial dependence and image analysis, while acyclic directed graphs (ADGs), which are especially conv ..."
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Cited by 49 (4 self)
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Graphical Markov models use graphs, either undirected, directed, or mixed, to represent possible dependences among statistical variables. Applications of undirected graphs (UDGs) include models for spatial dependence and image analysis, while acyclic directed graphs (ADGs), which are especially convenient for statistical analysis, arise in such fields as genetics and psychometrics and as models for expert systems and Bayesian belief networks. Lauritzen, Wermuth, and Frydenberg (LWF) introduced a Markov property for chain graphs, which are mixed graphs that can be used to represent simultaneously both causal and associative dependencies and which include both UDGs and ADGs as special cases. In this paper an alternative Markov property (AMP) for chain graphs is introduced, which in some ways is a more direct extension of the ADG Markov property than is the LWF property for chain graph. 1 INTRODUCTION Graphical Markov models use graphs, either undirected, directed, or mixed, to represent...
On the Markov Equivalence of Chain Graphs, Undirected Graphs, and Acyclic Digraphs
 Scandinavian Journal of Statistics
, 1994
"... Graphical Markov models use undirected graphs (UDGs), acyclic directed graphs (ADGs), or (mixed) chain graphs to represent possible dependencies among random variables in a multivariate distribution. Whereas a UDG is uniquely determined by its associated Markov model, this is not true for ADGs or fo ..."
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Cited by 30 (5 self)
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Graphical Markov models use undirected graphs (UDGs), acyclic directed graphs (ADGs), or (mixed) chain graphs to represent possible dependencies among random variables in a multivariate distribution. Whereas a UDG is uniquely determined by its associated Markov model, this is not true for ADGs or for general chain graphs (which include both UDGs and ADGs as special cases). This paper addresses three questions regarding the equivalence of graphical Markov models: when is a given chain graph Markov equivalent (1) to some UDG? (2) to some (at least one) ADG? (3) to some decomposable UDG? The answers are obtained by means of an extension of Frydenberg's (1990) elegant graphtheoretic characterization of the Markov equivalence of chain graphs. 1 Introduction The use of graphs to represent dependence relations among random variables, first introduced by Wright (1921), has generated considerable research activity, especially since the early 1980s. Particular attention has been devoted to gra...
Lectures on Contingency Tables
, 2002
"... The present set of lecture notes are prepared for the course “Statistik 2” at the University of Copenhagen. It is a revised version of notes prepared in connection with a series of lectures at the Swedish summerschool in Särö, June 11–17, 1979. The notes do by no means give a complete account of the ..."
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Cited by 18 (0 self)
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The present set of lecture notes are prepared for the course “Statistik 2” at the University of Copenhagen. It is a revised version of notes prepared in connection with a series of lectures at the Swedish summerschool in Särö, June 11–17, 1979. The notes do by no means give a complete account of the theory of contingency tables. They are based on the idea that the graph theoretic methods in Darroch, Lauritzen and Speed (1978) can be used directly to develop this theory and, hopefully, with some pedagogical advantages. My thanks are due to the audience at the Swedish summerschool for patiently listening to the first version of these lectures, to Joseph Verducci, Stanford, who read the manuscript and suggested many improvements and corrections, and to Ursula Hansen, who typed the manuscript.
dHugin: A computational system for dynamic timesliced Bayesian networks
, 1995
"... A computational system for reasoning about dynamic timesliced systems using Bayesian networks is presented. The system, called dHugin, may be viewed as a generalization of the inference methods of classical discrete timeseries analysis in the sense that it allows description of nonlinear, discret ..."
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Cited by 14 (0 self)
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A computational system for reasoning about dynamic timesliced systems using Bayesian networks is presented. The system, called dHugin, may be viewed as a generalization of the inference methods of classical discrete timeseries analysis in the sense that it allows description of nonlinear, discrete multivariate dynamic systems with complex conditional independence structures. The paper introduces the notions of dynamic timesliced Bayesian networks, a dynamic time window, and common operations on the time window. Inference, pertaining to the time window and time slices preceding it, are formulated in terms of the wellknown message passing scheme in junction trees [Jensen et al. (1990)]. Backward smoothing, for example, are performed efficiently through intertree message passing. Further, the system provides an ecient MonteCarlo algorithm for forecasting; i.e., inference pertaining to time slices succeeding the time window. The system has been implemented on top of the Hugin shell [Andersen et al. (1989)].
Multiscale Graphical Modeling in Space: Applications to Command and Control
, 2000
"... Recently, a class of multiscale treestructured models was introduced in terms of scalerecursive dynamics defined on trees. The main advantage of these models is their association with a fast, recursive, Kalmanfilter prediction algorithm. In this article, we propose a more general class of multisca ..."
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Cited by 9 (1 self)
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Recently, a class of multiscale treestructured models was introduced in terms of scalerecursive dynamics defined on trees. The main advantage of these models is their association with a fast, recursive, Kalmanfilter prediction algorithm. In this article, we propose a more general class of multiscale graphical models over acyclic directed graphs, for use in command and control problems. Moreover, we derive the generalizedKalmanfilter algorithm for graphical Markov models, which can be used to obtain the optimal predictors and prediction variances for multiscale graphical models. 1 Introduction Almost every aspect of command and control (C2) involves dealing with information in the presence of uncertainty. Since information in a battlefield is never precise, its status is rarely known exactly. In the face of this uncertainty, commanders must make decisions, issue orders, and monitor the consequences. The uncertainty may come from noisy data or, indeed, regions of the battle space whe...
Algorithms for Learning Decomposable Models and Chordal Graphs
, 1997
"... Decomposable dependency models and their graphical counterparts, i.e., chordal graphs, possess a number of interesting and useful properties. On the basis of two characterizations of decomposable models in terms of independence relationships, we develop an exact algorithm for recovering the chordal ..."
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Cited by 5 (0 self)
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Decomposable dependency models and their graphical counterparts, i.e., chordal graphs, possess a number of interesting and useful properties. On the basis of two characterizations of decomposable models in terms of independence relationships, we develop an exact algorithm for recovering the chordal graphical representation of any given decomposable model. We also propose an algorithm for learning chordal approximations of dependency models isomorphic to general undirected graphs. 1 INTRODUCTION Graphical models are knowledge representation tools used by an increasing number of researchers, particularly from the Uncertainty in Artificial Intelligence community. The reason for the success of graphical models is their capacity to represent and handle independence relationships (which have proved crucial for the efficient management and storage of information), as well as uncertain information. Among the different kinds of graphical models, we are particularly interested in undirected and...
Approximation of Bayesian networks through edge removals
, 1993
"... Due to the general inherent complexity of inference in Bayesian networks, the need to compromise the exactitude of inference arises frequently. A scheme for reduction of complexity by enforcing additional conditional independences is investigated. The enforcement of independences is achieved through ..."
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Cited by 5 (0 self)
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Due to the general inherent complexity of inference in Bayesian networks, the need to compromise the exactitude of inference arises frequently. A scheme for reduction of complexity by enforcing additional conditional independences is investigated. The enforcement of independences is achieved through edge removals in a triangulated graph. The removal of a single edge may imply an enormous reduction of complexity, since other edges may become superuous by its removal. The approximation scheme presented has several appealing features. Most notably among these, a bound on the overall approximation error can be computed locally, the bound on the error by a series of approximations equals the sum of the bounds of the errors of the individual approximations, and the influence of an approximation attenuates with increasing `distance' from edge removed. The scheme compares in some cases very favorably with the approximation method suggested by Jensen & Andersen (1990).