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27
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 563 (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.
Exploiting Causal Independence in Bayesian Network Inference
 Journal of Artificial Intelligence Research
, 1996
"... A new method is proposed for exploiting causal independencies in exact Bayesian network inference. ..."
Abstract

Cited by 156 (9 self)
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A new method is proposed for exploiting causal independencies in exact Bayesian network inference.
Stratified exponential families: Graphical models and model selection
 ANNALS OF STATISTICS
, 2001
"... ..."
Converting a rulebased expert system into a belief network
 Medical Informatics
, 1993
"... The theory of belief networks offers a relatively new approach for dealing with uncertain information in knowledgebased (expert) systems. In contrast with the heuristic techniques for reasoning with uncertainty employed in many rulebased expert systems, the theory of belief networks is mathematica ..."
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Cited by 37 (6 self)
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The theory of belief networks offers a relatively new approach for dealing with uncertain information in knowledgebased (expert) systems. In contrast with the heuristic techniques for reasoning with uncertainty employed in many rulebased expert systems, the theory of belief networks is mathematically sound, based on techniques from probability theory. It therefore seems attractive to convert existing rulebased expert systems into belief networks. In this article, we discuss the design of a belief network reformulation of the diagnostic rulebased expert system HEPAR. For the purpose of this experiment, we have studied several typical pieces of medical knowledge represented in the HEPAR system. It turned out that, due to the differences in the type of knowledge represented and in the formalism used to represent uncertainty, much of the medical knowledge required for building the belief network concerned could not be extracted from HEPAR. As a consequence, significant additional knowledge acquisition was required. However, the objects and attributes defined in the HEPAR system, as well as the conditions in production rules mentioning these objects and attributes were useful for guiding the selection of the statistical variables for building the belief network. The mapping of objects and attributes in HEPAR to statistical variables is discussed in detail.
Triangulation of Graphs  Algorithms Giving Small Total State Space
, 1990
"... The problem of achieving small total state space for triangulated belief graphs (networks) is considered. It is an NPcomplete problem to find a triangulation with minimum state space. Our interest ..."
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Cited by 35 (0 self)
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The problem of achieving small total state space for triangulated belief graphs (networks) is considered. It is an NPcomplete problem to find a triangulation with minimum state space. Our interest
Maximal Prime Subgraph Decomposition of Bayesian Networks
 IEEE Transactions on Systems, Man, and Cybernetics, B
, 1999
"... In this paper we present a method for decomposition of Bayesian networks into their maximal prime subgraphs. The correctness of the method is proven and results relating the maximal prime subgraph decomposition to the maximal complete subgraphs of the moral graph of the original Bayesian network ..."
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Cited by 28 (0 self)
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In this paper we present a method for decomposition of Bayesian networks into their maximal prime subgraphs. The correctness of the method is proven and results relating the maximal prime subgraph decomposition to the maximal complete subgraphs of the moral graph of the original Bayesian network are presented. The maximal prime subgraphs of a Bayesian network can be organized as a tree which can be used as the computational structure for lazy propagation. We have also identified a number of tasks performed on Bayesian networks that can benefit from maximal prime subgraph decomposition. These tasks include divide and conquer triangulation, hybrid propagation algorithms combining exact and approximative inference techniques, and incremental construction of junction trees. Finally, we present the results of a series empirical evaluations relating the accumulated number of variables in maximal prime subgraphs of equal size to the size of the maximal prime subgraphs. 1 1
Building probabilistic networks: where do the numbers come from?  a guide to the literature
 IEEE Transactions on Knowledge and Data Engineering
, 2000
"... Probabilistic networks are now fairly well established as practical representations of knowledge for reasoning under uncertainty, as demonstrated by an increasing number of successful applications in such domains as (medical) diagnosis and prognosis, planning, vision, ..."
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Cited by 28 (3 self)
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Probabilistic networks are now fairly well established as practical representations of knowledge for reasoning under uncertainty, as demonstrated by an increasing number of successful applications in such domains as (medical) diagnosis and prognosis, planning, vision,
Causal Probabilistic Networks With Both Discrete and Continuous Variables
, 1993
"... An extension of the expert system shell HUGIN to include continuous wriables, in the form of linear additive normally distributed variables, is presented. The ..."
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Cited by 18 (0 self)
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An extension of the expert system shell HUGIN to include continuous wriables, in the form of linear additive normally distributed variables, is presented. The
On the impact of causal independence
, 1998
"... Reasoning in Bayesian networks is exponential in a graph parameter w3 known as induced width (also known as treewidth and maxclique size). In this paper, we investigate the potential of causal independence (CI) for improving this performance. We consider several tasks, such as belief updating, ndi ..."
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Cited by 14 (4 self)
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Reasoning in Bayesian networks is exponential in a graph parameter w3 known as induced width (also known as treewidth and maxclique size). In this paper, we investigate the potential of causal independence (CI) for improving this performance. We consider several tasks, such as belief updating, nding a most probable explanation (MPE), nding a maximum aposteriori hypothesis (MAP), and nding the maximum expected utility (MEU). We show that exploiting CI in belief updating can signi cantly reduce the e ective w3, sometimes down to the induced width of the unmoralized network's graph. For example, for polytrees, CI reduces complexity from exponential to linear in the family size. Similar results hold for the MAP and MEU tasks, while the MPE task is less sensitive to CI. These enhancements are incorporated into bucketelimination algorithms based on known approaches of network transformations [10, 13] and elimination [18]. We provide an ordering heuristic which guarantees that exploiting CI will never hurt the performance. Finally, wediscuss an e cient wayof propagating evidence in CInetworks using arcconsistency, and apply this idea to noisyOR networks. The resulting algorithm generalizes the Quickscore algorithm [9] for BN2O networks. 1
Using Sensitivity Analysis for Efficient Quantification of a Belief Network
, 1999
"... Sensitivity analysis is a method to investigate the effects of varying a model's parameters on its predictions. It was recently suggested as a suitable means to facilitate quantifying the joint probability distribution of a Bayesian belief network. This article presents practical experience with ..."
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Cited by 9 (0 self)
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Sensitivity analysis is a method to investigate the effects of varying a model's parameters on its predictions. It was recently suggested as a suitable means to facilitate quantifying the joint probability distribution of a Bayesian belief network. This article presents practical experience with performing sensitivity analyses on a belief network in the field of medical prognosis and treatment planning. Three network quantifications with different levels of informedness were constructed. Two poorlyinformed quantifications were improved by replacing the most influential parameters with the corresponding parameter estimates from the wellinformed network quantification; these influential parameters were found by performing oneway sensitivity analyses. Subsequently, the results of the replacements were investigated by comparing network predictions. It was found that it may be sufficient to gather a limited number of highlyinformed network parameters to obtain a satisfying network quant...