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28
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 579 (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.
Stable Local Computation with Conditional Gaussian Distributions
 Statistics and Computing
, 1999
"... : This article describes a propagation scheme for Bayesian networks with conditional Gaussian distributions that does not have the numerical weaknesses of the scheme derived in Lauritzen (1992). The propagation architecture is that of Lauritzen and Spiegelhalter (1988). In addition to the means and ..."
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Cited by 63 (1 self)
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: This article describes a propagation scheme for Bayesian networks with conditional Gaussian distributions that does not have the numerical weaknesses of the scheme derived in Lauritzen (1992). The propagation architecture is that of Lauritzen and Spiegelhalter (1988). In addition to the means and variances provided by the previous algorithm, the new propagation scheme yields full local marginal distributions. The new scheme also handles linear deterministic relationships between continuous variables in the network specification. The new propagation scheme is in many ways faster and simpler than previous schemes and the method has been implemented in the most recent version of the HUGIN software. Key words: Artificial intelligence, Bayesian networks, CG distributions, Gaussian mixtures, probabilistic expert systems, propagation of evidence. 1 Introduction Bayesian networks have developed into an important tool for building systems for decision support in environments characterized by...
Graphical Models for Genetic Analyses
 STATISTTICAL SCIENCE
, 2003
"... This paper introduces graphical models as a natural environment in which to formulate and solve problems in genetics and related areas. Particular emphasis is given to the relationships among various local computation algorithms which have been developed within the hitherto mostly separate areas o ..."
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Cited by 30 (1 self)
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This paper introduces graphical models as a natural environment in which to formulate and solve problems in genetics and related areas. Particular emphasis is given to the relationships among various local computation algorithms which have been developed within the hitherto mostly separate areas of graphical models and genetics. The potential of graphical models is explored and illustrated through a number of example applications where the genetic element is substantial or dominating.
Soft Evidential Update for Probabilistic Multiagent Systems
 INTERNATIONAL JOURNAL OF APPROXIMATE REASONING
, 2000
"... We address the problem of updating a probability distribution represented by a Bayesian network upon presentation of soft evidence. Our motivation ..."
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Cited by 26 (5 self)
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We address the problem of updating a probability distribution represented by a Bayesian network upon presentation of soft evidence. Our motivation
Computation in Valuation Algebras
 IN HANDBOOK OF DEFEASIBLE REASONING AND UNCERTAINTY MANAGEMENT SYSTEMS, VOLUME 5: ALGORITHMS FOR UNCERTAINTY AND DEFEASIBLE REASONING
, 1999
"... Many different formalisms for treating uncertainty or, more generally, information and knowledge, have a common underlying algebraic structure. ..."
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Cited by 23 (4 self)
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Many different formalisms for treating uncertainty or, more generally, information and knowledge, have a common underlying algebraic structure.
A Comparison of LauritzenSpiegelhalter, Hugin, and ShenoyShafer Architectures for Computing Marginals of Probability Distributions
 Proceedings of the 14th Conference on Uncertainty in Artificial Intelligence (UAI98
, 1998
"... In the last decade, several architectures have been proposed for exact computation of marginals using local computation. In this paper, we compare three architecturesLauritzenSpiegelhalter, Hugin, and ShenoyShaferfrom the perspective of graphical structure for message propagation, messagepa ..."
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Cited by 23 (0 self)
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In the last decade, several architectures have been proposed for exact computation of marginals using local computation. In this paper, we compare three architecturesLauritzenSpiegelhalter, Hugin, and ShenoyShaferfrom the perspective of graphical structure for message propagation, messagepassing scheme, computational efficiency, and storage efficiency. 1 INTRODUCTION In the last decade, several architectures have been proposed in the uncertain reasoning literature for exact computation of marginals of multivariate discrete probability distributions. One of the pioneering architectures for computing marginals was proposed by Pearl [1986]. Pearl's architecture applies to singly connected Bayes nets. For multiply connected Bayes nets, Pearl [1986] proposed the method of conditioning to reduce a multiply connected Bayes net to several singly connected Bayes nets. In 1988, Lauritzen and Spiegelhalter [1988] proposed an alternative architecture for computing marginals that applies...
Unifying clustertree decompositions for reasoning in graphical models
 Artificial Intelligence
, 2005
"... The paper provides a unifying perspective of treedecomposition algorithms appearing in various automated reasoning areas such as jointree clustering for constraintsatisfaction and the cliquetree algorithm for probabilistic reasoning. Within this framework, we introduce a new algorithm, called bu ..."
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Cited by 18 (9 self)
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The paper provides a unifying perspective of treedecomposition algorithms appearing in various automated reasoning areas such as jointree clustering for constraintsatisfaction and the cliquetree algorithm for probabilistic reasoning. Within this framework, we introduce a new algorithm, called buckettree elimination (BT E), that extends Bucket Elimination (BE) to trees, and show that it can provide a speedup of n over BE for various reasoning tasks. Timespace tradeoffs of treedecomposition processing are analyzed. 1
Some improvements to the ShenoyShafer and Hugin architectures for computing marginals
 Artificial Intelligence
, 1998
"... The main aim of this paper is to describe two modifications to the ShenoyShafer architecture with the goal of making it computationally more efficient in computing marginals of the joint valuation. We also describe a modification to the Hugin architecture. Finally, we briefly compare the tradition ..."
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Cited by 15 (1 self)
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The main aim of this paper is to describe two modifications to the ShenoyShafer architecture with the goal of making it computationally more efficient in computing marginals of the joint valuation. We also describe a modification to the Hugin architecture. Finally, we briefly compare the traditional and modified architectures by solving a couple of small Bayesian networks, and conclude with a statement of further research. 1998 Elsevier Science B.V. All rights reserved.
A qualitative linear utility theory for Spohn’s theory of epistemic beliefs
 In UAI
, 2000
"... In this paper, we formulate a qualitative “linear” utility theory for lotteries in which uncertainty is expressed qualitatively using a Spohnian disbelief function. We argue that a rational decision maker facing an uncertain decision problem in which the uncertainty is expressed qualitatively should ..."
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Cited by 12 (4 self)
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In this paper, we formulate a qualitative “linear” utility theory for lotteries in which uncertainty is expressed qualitatively using a Spohnian disbelief function. We argue that a rational decision maker facing an uncertain decision problem in which the uncertainty is expressed qualitatively should behave so as to maximize “qualitative expected utility.” Our axiomatization of the qualitative utility is similar to the axiomatization developed by von Neumann and Morgenstern for probabilistic lotteries. We compare our results with other recent results in qualitative decision making. 1