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667
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 770 (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.
Constructing Free Energy Approximations and Generalized Belief Propagation Algorithms
 IEEE Transactions on Information Theory
, 2005
"... Important inference problems in statistical physics, computer vision, errorcorrecting coding theory, and artificial intelligence can all be reformulated as the computation of marginal probabilities on factor graphs. The belief propagation (BP) algorithm is an efficient way to solve these problems t ..."
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Cited by 585 (13 self)
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Important inference problems in statistical physics, computer vision, errorcorrecting coding theory, and artificial intelligence can all be reformulated as the computation of marginal probabilities on factor graphs. The belief propagation (BP) algorithm is an efficient way to solve these problems that is exact when the factor graph is a tree, but only approximate when the factor graph has cycles. We show that BP fixed points correspond to the stationary points of the Bethe approximation of the free energy for a factor graph. We explain how to obtain regionbased free energy approximations that improve the Bethe approximation, and corresponding generalized belief propagation (GBP) algorithms. We emphasize the conditions a free energy approximation must satisfy in order to be a “valid ” or “maxentnormal ” approximation. We describe the relationship between four different methods that can be used to generate valid approximations: the “Bethe method, ” the “junction graph method, ” the “cluster variation method, ” and the “region graph method.” Finally, we explain how to tell whether a regionbased approximation, and its corresponding GBP algorithm, is likely to be accurate, and describe empirical results showing that GBP can significantly outperform BP.
Belief Propagation
, 2010
"... When a pair of nuclearpowered Russian submarines was reported patrolling off the eastern seaboard of the U.S. last summer, Pentagon officials expressed wariness over the Kremlin’s motivations. At the same time, these officials emphasized their confidence in the U.S. Navy’s tracking capabilities: “W ..."
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Cited by 474 (11 self)
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When a pair of nuclearpowered Russian submarines was reported patrolling off the eastern seaboard of the U.S. last summer, Pentagon officials expressed wariness over the Kremlin’s motivations. At the same time, these officials emphasized their confidence in the U.S. Navy’s tracking capabilities: “We’ve known where they were,” a senior Defense Department official told the New York Times, “and we’re not concerned about our ability to track the subs.” While the official did not divulge the methods used by the Navy to track submarines, the Times added that such
Discriminative probabilistic models for relational data
, 2002
"... In many supervised learning tasks, the entities to be labeled are related to each other in complex ways and their labels are not independent. For example, in hypertext classification, the labels of linked pages are highly correlated. A standard approach is to classify each entity independently, igno ..."
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Cited by 415 (12 self)
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In many supervised learning tasks, the entities to be labeled are related to each other in complex ways and their labels are not independent. For example, in hypertext classification, the labels of linked pages are highly correlated. A standard approach is to classify each entity independently, ignoring the correlations between them. Recently, Probabilistic Relational Models, a relational version of Bayesian networks, were used to define a joint probabilistic model for a collection of related entities. In this paper, we present an alternative framework that builds on (conditional) Markov networks and addresses two limitations of the previous approach. First, undirected models do not impose the acyclicity constraint that hinders representation of many important relational dependencies in directed models. Second, undirected models are well suited for discriminative training, where we optimize the conditional likelihood of the labels given the features, which generally improves classification accuracy. We show how to train these models effectively, and how to use approximate probabilistic inference over the learned model for collective classification of multiple related entities. We provide experimental results on a webpage classification task, showing that accuracy can be significantly improved by modeling relational dependencies. 1
Correctness of belief propagation in Gaussian graphical models of arbitrary topology
 NEURAL COMPUTATION
, 1999
"... Local "belief propagation" rules of the sort proposed byPearl [12] are guaranteed to converge to the correct posterior probabilities in singly connected graphical models. Recently, a number of researchers have empirically demonstrated good performance of "loopy belief propagation&q ..."
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Cited by 296 (7 self)
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Local "belief propagation" rules of the sort proposed byPearl [12] are guaranteed to converge to the correct posterior probabilities in singly connected graphical models. Recently, a number of researchers have empirically demonstrated good performance of "loopy belief propagation"  using these same rules on graphs with loops. Perhaps the most dramatic instance is the near Shannonlimit performance of "Turbo codes", whose decoding algorithm is equivalentto loopy belief propagation. Except for the
On the Optimality of Solutions of the MaxProduct Belief Propagation Algorithm in Arbitrary Graphs
, 2001
"... Graphical models, suchasBayesian networks and Markov random fields, represent statistical dependencies of variables by a graph. The maxproduct "belief propagation" algorithm is a localmessage passing algorithm on this graph that is known to converge to a unique fixed point when the gra ..."
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Cited by 241 (13 self)
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Graphical models, suchasBayesian networks and Markov random fields, represent statistical dependencies of variables by a graph. The maxproduct "belief propagation" algorithm is a localmessage passing algorithm on this graph that is known to converge to a unique fixed point when the graph is a tree. Furthermore, when the graph is a tree, the assignment based on the fixedpoint yields the most probable a posteriori (MAP) values of the unobserved variables given the observed ones. Recently, good
Classification in Networked Data: A toolkit and a univariate case study
, 2006
"... This paper is about classifying entities that are interlinked with entities for which the class is known. After surveying prior work, we present NetKit, a modular toolkit for classification in networked data, and a casestudy of its application to networked data used in prior machine learning resear ..."
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Cited by 200 (10 self)
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This paper is about classifying entities that are interlinked with entities for which the class is known. After surveying prior work, we present NetKit, a modular toolkit for classification in networked data, and a casestudy of its application to networked data used in prior machine learning research. NetKit is based on a nodecentric framework in which classifiers comprise a local classifier, a relational classifier, and a collective inference procedure. Various existing nodecentric relational learning algorithms can be instantiated with appropriate choices for these components, and new combinations of components realize new algorithms. The case study focuses on univariate network classification, for which the only information used is the structure of class linkage in the network (i.e., only links and some class labels). To our knowledge, no work previously has evaluated systematically the power of classlinkage alone for classification in machine learning benchmark data sets. The results demonstrate that very simple networkclassification models perform quite well—well enough that they should be used regularly as baseline classifiers for studies of learning with networked data. The simplest method (which performs remarkably well) highlights the close correspondence between several existing methods introduced for different purposes—i.e., Gaussianfield classifiers, Hopfield networks, and relationalneighbor classifiers. The case study also shows that there are two sets of techniques that are preferable in different situations, namely when few versus many labels are known initially. We also demonstrate that link selection plays an important role similar to traditional feature selection.
Dynamic Conditional Random Fields: Factorized Probabilistic Models for Labeling and Segmenting Sequence Data
 IN ICML
, 2004
"... In sequence modeling, we often wish to represent complex interaction between labels, such as when performing multiple, cascaded labeling tasks on the same sequence, or when longrange dependencies exist. We present dynamic conditional random fields (DCRFs), a generalization of linearchain cond ..."
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Cited by 171 (13 self)
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In sequence modeling, we often wish to represent complex interaction between labels, such as when performing multiple, cascaded labeling tasks on the same sequence, or when longrange dependencies exist. We present dynamic conditional random fields (DCRFs), a generalization of linearchain conditional random fields (CRFs) in which each time slice contains a set of state variables and edgesa distributed state representation as in dynamic Bayesian networks (DBNs)and parameters are tied across slices. Since exact
Towards highly reliable enterprise network services via inference of multilevel dependencies
 IN SIGCOMM
, 2007
"... Localizing the sources of performance problems in large enterprise networks is extremely challenging. Dependencies are numerous, complex and inherently multilevel, spanning hardware and software components across the network and the computing infrastructure. To exploit these dependencies for fast, ..."
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Cited by 161 (10 self)
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Localizing the sources of performance problems in large enterprise networks is extremely challenging. Dependencies are numerous, complex and inherently multilevel, spanning hardware and software components across the network and the computing infrastructure. To exploit these dependencies for fast, accurate problem localization, we introduce an Inference Graph model, which is welladapted to userperceptible problems rooted in conditions giving rise to both partial service degradation and hard faults. Further, we introduce the Sherlock system to discover Inference Graphs in the operational enterprise, infer critical attributes, and then leverage the result to automatically detect and localize problems. To illuminate strengths and limitations of the approach, we provide results from a prototype deployment in a large enterprise network, as well as from testbed emulations and simulations. In particular, we find that taking into account multilevel structure leads to a 30 % improvement in fault localization, as compared to twolevel approaches.