Book•
Graphical Models in Applied Multivariate Statistics
01 Apr 1990-
TL;DR: This introduction to the use of graphical models in the description and modeling of multivariate systems covers conditional independence, several types of independence graphs, Gaussian models, issues in model selection, regression and decomposition.
Abstract: The Wiley Paperback Series makes valuable content more accessible to a new generation of statisticians, mathematicians and scientists.Graphical models--a subset of log-linear models--reveal the interrelationships between multiple variables and features of the underlying conditional independence. This introduction to the use of graphical models in the description and modeling of multivariate systems covers conditional independence, several types of independence graphs, Gaussian models, issues in model selection, regression and decomposition. Many numerical examples and exercises with solutions are included.This book is aimed at students who require a course on applied multivariate statistics unified by the concept of conditional independence and researchers concerned with applying graphical modelling techniques.
Citations
More filters
TL;DR: An overview of this emerging field is provided, clarifying how data mining and knowledge discovery in databases are related both to each other and to related fields, such as machine learning, statistics, and databases.
Abstract: ■ Data mining and knowledge discovery in databases have been attracting a significant amount of research, industry, and media attention of late. What is all the excitement about? This article provides an overview of this emerging field, clarifying how data mining and knowledge discovery in databases are related both to each other and to related fields, such as machine learning, statistics, and databases. The article mentions particular real-world applications, specific data-mining techniques, challenges involved in real-world applications of knowledge discovery, and current and future research directions in the field.
4,782 citations
Cites methods from "Graphical Models in Applied Multiva..."
...Graphic models specify probabilistic dependencies using a graph structure ( Whittaker 1990; Pearl 1988)....
[...]
TL;DR: In this paper, generalized linear mixed models (GLMM) are used to estimate the marginal quasi-likelihood for the mean parameters and the conditional variance for the variances, and the dispersion matrix is specified in terms of a rank deficient inverse covariance matrix.
Abstract: Statistical approaches to overdispersion, correlated errors, shrinkage estimation, and smoothing of regression relationships may be encompassed within the framework of the generalized linear mixed model (GLMM). Given an unobserved vector of random effects, observations are assumed to be conditionally independent with means that depend on the linear predictor through a specified link function and conditional variances that are specified by a variance function, known prior weights and a scale factor. The random effects are assumed to be normally distributed with mean zero and dispersion matrix depending on unknown variance components. For problems involving time series, spatial aggregation and smoothing, the dispersion may be specified in terms of a rank deficient inverse covariance matrix. Approximation of the marginal quasi-likelihood using Laplace's method leads eventually to estimating equations based on penalized quasilikelihood or PQL for the mean parameters and pseudo-likelihood for the variances. Im...
4,317 citations
TL;DR: In this paper, a nonparametric framework for causal inference is proposed, in which diagrams are queried to determine if the assumptions available are sufficient for identifying causal effects from nonexperimental data.
Abstract: SUMMARY The primary aim of this paper is to show how graphical models can be used as a mathematical language for integrating statistical and subject-matter information. In particular, the paper develops a principled, nonparametric framework for causal inference, in which diagrams are queried to determine if the assumptions available are sufficient for identifying causal effects from nonexperimental data. If so the diagrams can be queried to produce mathematical expressions for causal effects in terms of observed distributions; otherwise, the diagrams can be queried to suggest additional observations or auxiliary experiments from which the desired inferences can be obtained.
2,209 citations
Cites methods from "Graphical Models in Applied Multiva..."
...[Whittaker 1990] Whittaker, J., Graphical Models in Applied Multivariate Statistics,John Wiley and Sons, Chichester, England, 1990....
[...]
TL;DR: The implementation of the penalized likelihood methods for estimating the concentration matrix in the Gaussian graphical model is nontrivial, but it is shown that the computation can be done effectively by taking advantage of the efficient maxdet algorithm developed in convex optimization.
Abstract: SUMMARY We propose penalized likelihood methods for estimating the concentration matrix in the Gaussian graphical model. The methods lead to a sparse and shrinkage estimator of the concentration matrix that is positive definite, and thus conduct model selection and estimation simultaneously. The implementation of the methods is nontrivial because of the positive definite constraint on the concentration matrix, but we show that the computation can be done effectively by taking advantage of the efficient maxdet algorithm developed in convex optimization. We propose a BIC-type criterion for the selection of the tuning parameter in the penalized likelihood methods. The connection between our methods and existing methods is illustrated. Simulations and real examples demonstrate the competitive performance of the new methods.
1,824 citations
Cites background from "Graphical Models in Applied Multiva..."
...…Access published February 28, 2007 at P ennsylvania S tate U niversity on A ugust 19, 2010 http://biom et.oxfordjournals.org D ow nloaded from see Whittaker (1990), Lauritzen (1996) and Edwards (2000) for statistical properties of Gaussian concentration graph models and commonly used model…...
[...]
TL;DR: A review of machine learning methods employing positive definite kernels, ranging from binary classifiers to sophisticated methods for estimation with structured data, which include nonlinear functions as well as functions defined on nonvectorial data.
Abstract: We review machine learning methods employing positive definite kernels. These methods formulate learning and estimation problems in a reproducing kernel Hilbert space (RKHS) of functions defined on the data domain, expanded in terms of a kernel. Working in linear spaces of function has the benefit of facilitating the construction and analysis of learning algorithms while at the same time allowing large classes of functions. The latter include nonlinear functions as well as functions defined on nonvectorial data. We cover a wide range of methods, ranging from binary classifiers to sophisticated methods for estimation with structured data.
1,791 citations
References
More filters
Journal Article•
TL;DR: In this paper, a vue d'ensemble de la theorie mathematique et statistique des modeles d'association graphiques mixtes, concernes par la description dassociations entre variables, ou certaines sont admises etre quantitatives et d'autres qualitatives.
Abstract: On donne une vue d'ensemble de la theorie mathematique et statistique des modeles d'association graphiques mixtes, concernes par la description d'associations entre variables, ou certaines sont admises etre quantitatives et d'autres qualitatives. Tous ces modeles (ayant ses origines en particulier en physique statistique et en genetique) sont determines par des restrictions de type distributionnel complete par des restrictions d'independance conditionnelle. Ils elargissent et unifient un certain nombre de techniques statistiques qui sont bien etablies, surtout en sciences sociales. L'article est suivi de discussions et de commentaires
49 citations