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705
Learning in graphical models
 STATISTICAL SCIENCE
, 2004
"... Statistical applications in fields such as bioinformatics, information retrieval, speech processing, image processing and communications often involve largescale models in which thousands or millions of random variables are linked in complex ways. Graphical models provide a general methodology for ..."
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Cited by 800 (10 self)
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Statistical applications in fields such as bioinformatics, information retrieval, speech processing, image processing and communications often involve largescale models in which thousands or millions of random variables are linked in complex ways. Graphical models provide a general methodology for approaching these problems, and indeed many of the models developed by researchers in these applied fields are instances of the general graphical model formalism. We review some of the basic ideas underlying graphical models, including the algorithmic ideas that allow graphical models to be deployed in largescale data analysis problems. We also present examples of graphical models in bioinformatics, errorcontrol coding and language processing.
Image Parsing: Unifying Segmentation, Detection, and Recognition
, 2005
"... In this paper we present a Bayesian framework for parsing images into their constituent visual patterns. The parsing algorithm optimizes the posterior probability and outputs a scene representation in a "parsing graph", in a spirit similar to parsing sentences in speech and natural lang ..."
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Cited by 234 (21 self)
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In this paper we present a Bayesian framework for parsing images into their constituent visual patterns. The parsing algorithm optimizes the posterior probability and outputs a scene representation in a "parsing graph", in a spirit similar to parsing sentences in speech and natural language. The algorithm constructs the parsing graph and reconfigures it dynamically using a set of reversible Markov chain jumps. This computational framework integrates two popular inference approaches  generative (topdown) methods and discriminative (bottomup) methods. The former formulates the posterior probability in terms of generative models for images defined by likelihood functions and priors. The latter computes discriminative probabilities based on a sequence (cascade) of bottomup tests/filters.
A tutorial on particle filtering and smoothing: fifteen years later
 OXFORD HANDBOOK OF NONLINEAR FILTERING
, 2011
"... Optimal estimation problems for nonlinear nonGaussian statespace models do not typically admit analytic solutions. Since their introduction in 1993, particle filtering methods have become a very popular class of algorithms to solve these estimation problems numerically in an online manner, i.e. r ..."
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Cited by 206 (15 self)
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Optimal estimation problems for nonlinear nonGaussian statespace models do not typically admit analytic solutions. Since their introduction in 1993, particle filtering methods have become a very popular class of algorithms to solve these estimation problems numerically in an online manner, i.e. recursively as observations become available, and are now routinely used in fields as diverse as computer vision, econometrics, robotics and navigation. The objective of this tutorial is to provide a complete, uptodate survey of this field as of 2008. Basic and advanced particle methods for filtering as well as smoothing are presented.
Fastest mixing markov chain on a graph
 SIAM Review
"... Author names in alphabetical order. Submitted to SIAM Review, problems and techniques section. We consider a symmetric random walk on a connected graph, where each edge is labeled with the probability of transition between the two adjacent vertices. The associated Markov chain has a uniform equilibr ..."
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Cited by 157 (16 self)
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Author names in alphabetical order. Submitted to SIAM Review, problems and techniques section. We consider a symmetric random walk on a connected graph, where each edge is labeled with the probability of transition between the two adjacent vertices. The associated Markov chain has a uniform equilibrium distribution; the rate of convergence to this distribution, i.e., the mixing rate of the Markov chain, is determined by the second largest (in magnitude) eigenvalue of the transition matrix. In this paper we address the problem of assigning probabilities to the edges of the graph in such a way as to minimize the second largest magnitude eigenvalue, i.e., the problem of ¯nding the fastest mixing Markov chain on the graph. We show that this problem can be formulated as a convex optimization problem, which can in turn be expressed as a semide¯nite program (SDP). This allows us to easily compute the (globally) fastest mixing Markov chain for any graph with a modest number of edges (say, 1000) using standard numerical methods for SDPs. Larger problems can be solved by
Parameter estimation for text analysis
, 2004
"... Abstract. Presents parameter estimation methods common with discrete probability distributions, which is of particular interest in text modeling. Starting with maximum likelihood, a posteriori and Bayesian estimation, central concepts like conjugate distributions and Bayesian networks are reviewed. ..."
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Cited by 117 (0 self)
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Abstract. Presents parameter estimation methods common with discrete probability distributions, which is of particular interest in text modeling. Starting with maximum likelihood, a posteriori and Bayesian estimation, central concepts like conjugate distributions and Bayesian networks are reviewed. As an application, the model of latent Dirichlet allocation (LDA) is explained in detail with a full derivation of an approximate inference algorithm based on Gibbs sampling, including a discussion of Dirichlet hyperparameter estimation. Finally, analysis methods of LDA models are discussed.
A Stochastic Grammar of Images
 Foundations and Trends in Computer Graphics and Vision
, 2006
"... This exploratory paper quests for a stochastic and context sensitive grammar of images. The grammar should achieve the following four objectives and thus serves as a unified framework of representation, learning, and recognition for a large number of object categories. (i) The grammar represents bot ..."
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Cited by 117 (26 self)
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This exploratory paper quests for a stochastic and context sensitive grammar of images. The grammar should achieve the following four objectives and thus serves as a unified framework of representation, learning, and recognition for a large number of object categories. (i) The grammar represents both the hierarchical decompositions from scenes, to objects, parts, primitives and pixels by terminal and nonterminal nodes and the contexts for spatial and functional relations by horizontal links between the nodes. It formulates each object category as the set of all possible valid configurations produced by the grammar. (ii) The grammar is embodied in a simple And–Or graph representation where each Ornode points to alternative subconfigurations and an Andnode is decomposed into a number of components. This representation supports recursive topdown/bottomup procedures for image parsing under the Bayesian framework and make it convenient to scale
Error bounds for computing the expectation by Markov chain Monte Carlo
, 2009
"... We study the error of reversible Markov chain Monte Carlo methods for approximating the expectation of a function. Explicit error bounds with respect to the l2, l4 and l∞norm of the function are proven. By the estimation the well known asymptotical limit of the error is attained, i.e. there is n ..."
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Cited by 116 (2 self)
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We study the error of reversible Markov chain Monte Carlo methods for approximating the expectation of a function. Explicit error bounds with respect to the l2, l4 and l∞norm of the function are proven. By the estimation the well known asymptotical limit of the error is attained, i.e. there is no gap between the estimate and the asymptotical behavior. We discuss the dependence of the error on a burnin of the Markov chain. Furthermore we suggest and justify a specific burnin for optimizing the algorithm.
Markov Chain Monte Carlo methods and the label switching problem in Bayesian mixture modelling
 Statistical Science
"... Abstract. In the past ten years there has been a dramatic increase of interest in the Bayesian analysis of finite mixture models. This is primarily because of the emergence of Markov chain Monte Carlo (MCMC) methods. While MCMC provides a convenient way to draw inference from complicated statistical ..."
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Cited by 113 (5 self)
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Abstract. In the past ten years there has been a dramatic increase of interest in the Bayesian analysis of finite mixture models. This is primarily because of the emergence of Markov chain Monte Carlo (MCMC) methods. While MCMC provides a convenient way to draw inference from complicated statistical models, there are many, perhaps underappreciated, problems associated with the MCMC analysis of mixtures. The problems are mainly caused by the nonidentifiability of the components under symmetric priors, which leads to socalled label switching in the MCMC output. This means that ergodic averages of component specific quantities will be identical and thus useless for inference. We review the solutions to the label switching problem, such as artificial identifiability constraints, relabelling algorithms and label invariant loss functions. We also review various MCMC sampling schemes that have been suggested for mixture models and discuss posterior sensitivity to prior specification.
Marginalized particle filters for mixed linear/nonlinear statespace models
 IEEE Transactions on Signal Processing
, 2005
"... Abstract—The particle filter offers a general numerical tool to approximate the posterior density function for the state in nonlinear and nonGaussian filtering problems. While the particle filter is fairly easy to implement and tune, its main drawback is that it is quite computer intensive, with th ..."
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Cited by 112 (33 self)
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Abstract—The particle filter offers a general numerical tool to approximate the posterior density function for the state in nonlinear and nonGaussian filtering problems. While the particle filter is fairly easy to implement and tune, its main drawback is that it is quite computer intensive, with the computational complexity increasing quickly with the state dimension. One remedy to this problem is to marginalize out the states appearing linearly in the dynamics. The result is that one Kalman filter is associated with each particle. The main contribution in this paper is the derivation of the details for the marginalized particle filter for a general nonlinear statespace model. Several important special cases occurring in typical signal processing applications will also be discussed. The marginalized particle filter is applied to an integrated navigation system for aircraft. It is demonstrated that the complete highdimensional system can be based on a particle filter using marginalization for all but three states. Excellent performance on real flight data is reported. Index Terms—Kalman filter, marginalization, navigation systems, nonlinear systems, particle filter, state estimation. I.