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60
Operations for Learning with Graphical Models
 Journal of Artificial Intelligence Research
, 1994
"... This paper is a multidisciplinary review of empirical, statistical learning from a graphical model perspective. Wellknown examples of graphical models include Bayesian networks, directed graphs representing a Markov chain, and undirected networks representing a Markov field. These graphical models ..."
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Cited by 277 (13 self)
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This paper is a multidisciplinary review of empirical, statistical learning from a graphical model perspective. Wellknown examples of graphical models include Bayesian networks, directed graphs representing a Markov chain, and undirected networks representing a Markov field. These graphical models are extended to model data analysis and empirical learning using the notation of plates. Graphical operations for simplifying and manipulating a problem are provided including decomposition, differentiation, and the manipulation of probability models from the exponential family. Two standard algorithm schemas for learning are reviewed in a graphical framework: Gibbs sampling and the expectation maximization algorithm. Using these operations and schemas, some popular algorithms can be synthesized from their graphical specification. This includes versions of linear regression, techniques for feedforward networks, and learning Gaussian and discrete Bayesian networks from data. The paper conclu...
Training Conditional Random Fields via Gradient Tree Boosting
 In Proceedings of the 21th International Conference on Machine Learning (ICML
, 2004
"... Conditional Random Fields (CRFs; Lafferty, McCallum, & Pereira, 2001) provide a flexible and powerful model for learning to assign labels to elements of sequences in such applications as partofspeech tagging, texttospeech mapping, protein and DNA sequence analysis, and information extraction ..."
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Cited by 79 (2 self)
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Conditional Random Fields (CRFs; Lafferty, McCallum, & Pereira, 2001) provide a flexible and powerful model for learning to assign labels to elements of sequences in such applications as partofspeech tagging, texttospeech mapping, protein and DNA sequence analysis, and information extraction from web pages. However, existing learning algorithms are slow, particularly in problems with large numbers of potential input features. This paper describes a new method...
Texture Synthesis via a Noncausal Nonparametric Multiscale Markov Random Field
, 1998
"... Our noncausal, nonparametric, multiscale, Markov random field (MRF) model is capable of synthesising and capturing the characteristics of a wide variety of textures, from the highly structured to the stochastic. We use a multiscale synthesis algorithm incorporating local annealing to obtain larger r ..."
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Cited by 67 (7 self)
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Our noncausal, nonparametric, multiscale, Markov random field (MRF) model is capable of synthesising and capturing the characteristics of a wide variety of textures, from the highly structured to the stochastic. We use a multiscale synthesis algorithm incorporating local annealing to obtain larger realisations of texture visually indistinguishable from the training texture.
Chain Graphs for Learning
 In Uncertainty in Artificial Intelligence
, 1995
"... Chain graphs combine directed and undirected graphs and their underlying mathematics combines properties of the two. This paper gives a simplified definition of chain graphs based on a hierarchical combination of Bayesian (directed) and Markov (undirected) networks. Examples of a chain graph are mul ..."
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Cited by 37 (1 self)
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Chain graphs combine directed and undirected graphs and their underlying mathematics combines properties of the two. This paper gives a simplified definition of chain graphs based on a hierarchical combination of Bayesian (directed) and Markov (undirected) networks. Examples of a chain graph are multivariate feedforward networks, clustering with conditional interaction between variables, and forms of Bayes classifiers. Chain graphs are then extended using the notation of plates so that samples and data analysis problems can be represented in a graphical model as well. Implications for learning are discussed in the conclusion. 1 Introduction Probabilistic networks are a notational device that allow one to abstract forms of probabilistic reasoning without getting lost in the mathematical detail of the underlying equations. They offer a framework whereby many forms of probabilistic reasoning can be combined and performed on probabilistic models without careful hand programming. Efforts ...
Binary Partitioning, Perceptual Grouping, and Restoration with Semidefinite Programming
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 2003
"... We introduce a novel optimization method based on semidefinite programming relaxations to the field of computer vision and apply it to the combinatorial problem of minimizing quadratic functionals in binary decision variables subject to linear constraints. ..."
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Cited by 35 (6 self)
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We introduce a novel optimization method based on semidefinite programming relaxations to the field of computer vision and apply it to the combinatorial problem of minimizing quadratic functionals in binary decision variables subject to linear constraints.
On The Convergence Of Markovian Stochastic Algorithms With Rapidly Decreasing Ergodicity Rates
 STOCHASTICS AND STOCHASTICS MODELS
, 1999
"... We analyse the convergence of stochastic algorithms with Markovian noise when the ergodicity of the Markov chain governing the noise rapidly decreases as the control parameter tends to infinity. In such a case, there may be a positive probability of divergence of the algorithm in the classic Robbins ..."
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Cited by 33 (1 self)
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We analyse the convergence of stochastic algorithms with Markovian noise when the ergodicity of the Markov chain governing the noise rapidly decreases as the control parameter tends to infinity. In such a case, there may be a positive probability of divergence of the algorithm in the classic RobbinsMonro form. We provide modifications of the algorithm which ensure convergence. Moreover, we analyse the asymptotic behaviour of these algorithms and state a diffusion approximation theorem.
Chordal Completions of Planar Graphs
, 1994
"... We prove that every planar graph on n vertices is contained in a chordal graph with at most cn log n edges for some absolute constant c and this is best possible to within a constant factor. ..."
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Cited by 25 (0 self)
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We prove that every planar graph on n vertices is contained in a chordal graph with at most cn log n edges for some absolute constant c and this is best possible to within a constant factor.
Bayesian Estimation for Homogeneous and Inhomogeneous Gaussian Random Fields
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1996
"... This paper investigates Bayesian estimation for Gaussian Markov random fields. In particular, a new class of inhomogeneous model is proposed. This inhomogeneous model uses a Markov random field to describe spatial variation of the smoothing parameter in a second random field which describes the spat ..."
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Cited by 24 (2 self)
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This paper investigates Bayesian estimation for Gaussian Markov random fields. In particular, a new class of inhomogeneous model is proposed. This inhomogeneous model uses a Markov random field to describe spatial variation of the smoothing parameter in a second random field which describes the spatial variation in the observed intensity image. The coupled Markov random fields will be used as prior distributions, and combined with Gaussian noise models to produce posterior distributions on which estimation will be based. All model parameters are estimated, in a fully Bayesian setting, using the MetropolisHastings algorithm. The models and algorithms will be illustrated using various artificial examples. The full posterior estimation procedures using homogeneous and inhomogeneous models will be compared. For the examples considered the fully Bayesian estimation for inhomogeneous models performs very favourably when compared to methods using homogeneous models, allowing differential smo...
The Equivalence of HalfQuadratic Minimization and the Gradient Linearization Iteration
"... A popular way to restore images comprising edges is to minimize a costfunction combining a quadratic datafidelity term and an edgepreserving (possibly nonconvex) regularization term. Mainly because of the latter term, the calculation of the solution is slow and cumbersome. Halfquadratic (HQ) min ..."
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Cited by 21 (4 self)
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A popular way to restore images comprising edges is to minimize a costfunction combining a quadratic datafidelity term and an edgepreserving (possibly nonconvex) regularization term. Mainly because of the latter term, the calculation of the solution is slow and cumbersome. Halfquadratic (HQ) minimization (multiplicative form) was pioneered by Geman and Reynolds (1992) in order to alleviate the computational task in the context of image reconstruction with nonconvex regularization. By promoting the idea of locally homogeneous image models with a continuousvalued line process, they reformulated the optimization problem in terms of an augmented cost function which is quadratic with respect to the image and separable with respect to the line process. Hence the name “half quadratic”. Since then, a large amount of papers were dedicated to HQ minimization and important results including edgepreservation along with convex regularization and convergence have been obtained. In this paper we show that HQ minimization (multiplicative form) is equivalent to the most simple and basic method where the gradient of the costfunction is linearized at each iteration step. In fact, both methods give exactly the same iterations. Furthermore, connections of HQ minimization with other methods, such as the quasiNewton method and the generalized Weiszfeld’s method, are straightforward.
Fast approximate maximum a posteriori restoration of multicolour images
, 1995
"... Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at ..."
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Cited by 15 (0 self)
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