This paper is a multidisciplinary review of empirical, statistical learning from a graphical model perspective. Well-known 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 feed-forward networks, and learning Gaussian and discrete Bayesian networks from data. The paper conclu...

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 part-of-speech tagging, text-to-speech 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...

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.

Abstract. This paper addresses two central problems for probabilistic processing models: parameter estimation from incomplete data and efficient retrieval of most probable analyses. These questions have been answered satisfactorily only for probabilistic regular and context-free models. We address these problems for a more expressive probabilistic constraint logic programming model. We present a log-linear probability model for probabilistic constraint logic programming. On top of this model we define an algorithm to estimate the parameters and to select the properties of log-linear models from incomplete data. This algorithm is an extension of the improved iterative scaling algorithm of Della Pietra, Della Pietra, and Lafferty (1995). Our algorithm applies to loglinear models in general and is accompanied with suitable approximation methods when applied to large data spaces. Furthermore, we present an approach for searching for most probable analyses of the probabilistic constraint logic programming model. This method can be applied to the ambiguity resolution problem in natural language processing applications. 1.

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 feed-forward 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 ...

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.

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-Monro 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.

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 Metropolis-Hastings 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...

Abstract not found

this article is to discuss general reasons for this prominence of MCMC, to give an overview of a variety of image models and the use made of MCMC methods in dealing with them, to describe two applications in more detail, To appear as a chapter in the book Practical Markov chain Monte Carlo, edited by W. Gilks, S. Richardson and D. Spiegelhalter, published by Chapman and Hall.