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113
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.
Tractable inference for complex stochastic processes
 In Proc. UAI
, 1998
"... The monitoring and control of any dynamic system depends crucially on the ability to reason about its current status and its future trajectory. In the case of a stochastic system, these tasks typically involve the use of a belief state—a probability distribution over the state of the process at a gi ..."
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Cited by 265 (13 self)
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The monitoring and control of any dynamic system depends crucially on the ability to reason about its current status and its future trajectory. In the case of a stochastic system, these tasks typically involve the use of a belief state—a probability distribution over the state of the process at a given point in time. Unfortunately, the state spaces of complex processes are very large, making an explicit representation of a belief state intractable. Even in dynamic Bayesian networks (DBNs), where the process itself can be represented compactly, the representation of the belief state is intractable. We investigate the idea of maintaining a compact approximation to the true belief state, and analyze the conditions under which the errors due to the approximations taken over the lifetime of the process do not accumulate to make our answers completely irrelevant. We show that the error in a belief state contracts exponentially as the process evolves. Thus, even with multiple approximations, the error in our process remains bounded indefinitely. We show how the additional structure of a DBN can be used to design our approximation scheme, improving its performance significantly. We demonstrate the applicability of our ideas in the context of a monitoring task, showing that orders of magnitude faster inference can be achieved with only a small degradation in accuracy. 1
The Bayes Net Toolbox for MATLAB
 Computing Science and Statistics
, 2001
"... The Bayes Net Toolbox (BNT) is an opensource Matlab package for directed graphical models. BNT supports many kinds of nodes (probability distributions), exact and approximate inference, parameter and structure learning, and static and dynamic models. BNT is widely used in teaching and research: the ..."
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Cited by 176 (2 self)
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The Bayes Net Toolbox (BNT) is an opensource Matlab package for directed graphical models. BNT supports many kinds of nodes (probability distributions), exact and approximate inference, parameter and structure learning, and static and dynamic models. BNT is widely used in teaching and research: the web page has received over 28,000 hits since May 2000. In this paper, we discuss a broad spectrum of issues related to graphical models (directed and undirected), and describe, at a highlevel, how BNT was designed to cope with them all. We also compare BNT to other software packages for graphical models, and to the nascent OpenBayes effort.
Modelling gene expression data using dynamic bayesian networks
, 1999
"... Recently, there has been much interest in reverse engineering genetic networks from time series data. In this paper, we show that most of the proposed discrete time models — including the boolean network model [Kau93, SS96], the linear model of D’haeseleer et al. [DWFS99], and the nonlinear model of ..."
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Cited by 157 (1 self)
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Recently, there has been much interest in reverse engineering genetic networks from time series data. In this paper, we show that most of the proposed discrete time models — including the boolean network model [Kau93, SS96], the linear model of D’haeseleer et al. [DWFS99], and the nonlinear model of Weaver et al. [WWS99] — are all special cases of a general class of models called Dynamic Bayesian Networks (DBNs). The advantages of DBNs include the ability to model stochasticity, to incorporate prior knowledge, and to handle hidden variables and missing data in a principled way. This paper provides a review of techniques for learning DBNs. Keywords: Genetic networks, boolean networks, Bayesian networks, neural networks, reverse engineering, machine learning. 1
A differential approach to inference in Bayesian networks
 Journal of the ACM
, 2000
"... We present a new approach to inference in Bayesian networks which is based on representing the network using a polynomial and then retrieving answers to probabilistic queries by evaluating and differentiating the polynomial. The network polynomial itself is exponential in size, but we show how it ca ..."
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Cited by 112 (18 self)
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We present a new approach to inference in Bayesian networks which is based on representing the network using a polynomial and then retrieving answers to probabilistic queries by evaluating and differentiating the polynomial. The network polynomial itself is exponential in size, but we show how it can be computed efficiently using an arithmetic circuit that can be evaluated and differentiated in time and space linear in the circuit size. The proposed framework for inference subsumes one of the most influential methods for inference in Bayesian networks, known as the tree–clustering or jointree method, which provides a deeper understanding of this classical method and lifts its desirable characteristics to a much more general setting. We discuss some theoretical and practical implications of this subsumption. 1.
Collective classification in network data
, 2008
"... Numerous realworld applications produce networked data such as web data (hypertext documents connected via hyperlinks) and communication networks (people connected via communication links). A recent focus in machine learning research has been to extend traditional machine learning classification te ..."
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Cited by 98 (27 self)
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Numerous realworld applications produce networked data such as web data (hypertext documents connected via hyperlinks) and communication networks (people connected via communication links). A recent focus in machine learning research has been to extend traditional machine learning classification techniques to classify nodes in such data. In this report, we attempt to provide a brief introduction to this area of research and how it has progressed during the past decade. We introduce four of the most widely used inference algorithms for classifying networked data and empirically compare them on both synthetic and realworld data. 1
ModelBased Diagnosis using Structured System Descriptions
 Journal of Artificial Intelligence Research
, 1996
"... This paper presents a comprehensive approach for modelbased diagnosis which includes proposals for characterizing and computing preferred diagnoses, assuming that the system description is augmented with a system structure (a directed graph explicating the interconnections between system compone ..."
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Cited by 58 (10 self)
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This paper presents a comprehensive approach for modelbased diagnosis which includes proposals for characterizing and computing preferred diagnoses, assuming that the system description is augmented with a system structure (a directed graph explicating the interconnections between system components). Specifically, we first introduce the notion of a consequence, which is a syntactically unconstrained propositional sentence that characterizes all consistencybased diagnoses and show that standard characterizations of diagnoses, such as minimal conflicts, correspond to syntactic variations on a consequence. Second, we propose a new syntactic variation on the consequence known as negation normal form (NNF) and discuss its merits compared to standard variations. Third, we introduce a basic algorithm for computing consequences in NNF given a structured system description. We show that if the system structure does not contain cycles, then there is always a linearsize consequence...
Value Elimination: Bayesian Inference via Backtracking Search
 IN UAI03
, 2003
"... We present Value Elimination, a new algorithm for Bayesian Inference. Given the same variable ordering information, Value Elimination can achieve performance that is within a constant factor of variable elimination or recursive conditioning, and on some problems it can perform exponentially bet ..."
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Cited by 49 (2 self)
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We present Value Elimination, a new algorithm for Bayesian Inference. Given the same variable ordering information, Value Elimination can achieve performance that is within a constant factor of variable elimination or recursive conditioning, and on some problems it can perform exponentially better, irrespective of the variable ordering used by these algorithms. Value Elimination
Hybrid Bayesian Networks for Reasoning about Complex Systems
, 2002
"... Many realworld systems are naturally modeled as hybrid stochastic processes, i.e., stochastic processes that contain both discrete and continuous variables. Examples include speech recognition, target tracking, and monitoring of physical systems. The task is usually to perform probabilistic inferen ..."
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Cited by 48 (0 self)
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Many realworld systems are naturally modeled as hybrid stochastic processes, i.e., stochastic processes that contain both discrete and continuous variables. Examples include speech recognition, target tracking, and monitoring of physical systems. The task is usually to perform probabilistic inference, i.e., infer the hidden state of the system given some noisy observations. For example, we can ask what is the probability that a certain word was pronounced given the readings of our microphone, what is the probability that a submarine is trying to surface given our sonar data, and what is the probability of a valve being open given our pressure and flow readings. Bayesian networks are
Beyond trees: Common factor models for 2D human pose recovery
 In ICCV
, 2005
"... Tree structured models have been widely used for determining the pose of a human body, from either 2D or 3D data. While such models can effectively represent the kinematic constraints of the skeletal structure, they do not capture additional constraints such as coordination of the limbs. Tree struct ..."
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Cited by 48 (1 self)
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Tree structured models have been widely used for determining the pose of a human body, from either 2D or 3D data. While such models can effectively represent the kinematic constraints of the skeletal structure, they do not capture additional constraints such as coordination of the limbs. Tree structured models thus miss an important source of information about human body pose, as limb coordination is necessary for balance while standing, walking, or running, as well as being evident in other activities such as dancing and throwing. In this paper we consider the use of undirected graphical models that augment a tree structure with latent variables in order to account for coordination between limbs. We refer to these as commonfactor models, since they are constructed by using factor analysis to identify additional correlations in limb position that are not accounted for by the kinematic tree structure. These commonfactor models have an underlying tree structure and thus a variant of the standard Viterbi algorithm for a tree can be applied for efficient estimation. We present some experimental results contrasting commonfactor models with tree models, and quantify the improvement in pose estimation for 2D image data. 1.