Building hyper Dirichlet processes for graphical models
TL;DR: In this paper, the authors explore graphical models based on a nonparametric family of distributions, developed from Dirichlet processes, and explore a prior over the graphical model if the random marginals also satisfy the independence constraints.
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Abstract: Graphical models are used to describe the conditional independence relations in multivariate data. They have been used for a variety of problems, including log-linear models (Liu and Massam, 2006), network analysis (Holland and Leinhardt, 1981; Strauss and Ikeda, 1990; Wasserman and Pattison, 1996; Pattison and Wasserman, 1999; Robins et al., 1999), graphical Gaussian models (Roverato and Whittaker, 1998; Giudici and Green, 1999; Marrelec and Benali, 2006), and genetics (Dobra et al., 2004). A distribution that satisfies the conditional independence structure of a graph is Markov. A graphical model is a family of distributions that is restricted to be Markov with respect to a certain graph. In a Bayesian problem, one may specify a prior over the graphical model. Such a prior is called a hyper Markov law if the random marginals also satisfy the independence constraints. Previous work in this area includes (Dempster, 1972; Dawid and Lauritzen, 1993; Giudici and Green, 1999; Letac and Massam, 2007). We explore graphical models based on a non-parametric family of distributions, developed from Dirichlet processes.
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Citations
Sparse covariance estimation in heterogeneous samples
TL;DR: In this article, the authors explore mixtures of Gaussian graphical models and infinite hidden Markov models where the emission distributions correspond to Gaussian graph models, allowing them to divide a heterogeneous population into homogeneous groups, with each cluster having its own conditional independence structure.
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Sparse covariance estimation in heterogeneous samples
TL;DR: This work considers both infinite mixtures and infinite hidden Markov models where the emission distributions correspond to Gaussian graphical models, allowing us to divide a heterogeneous population into homogenous groups, with each cluster having its own conditional independence structure.
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•Proceedings Article
Bayesian Nonparametric Models on Decomposable Graphs
François Caron,Arnaud Doucet +1 more
- 07 Dec 2009
TL;DR: Extensions of Dirichlet processes where the dependency between samples is given by a known decomposable graph are proposed, which have appealing properties and can be easily learned using Monte Carlo techniques.
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Inference of global clusters from locally distributed data
TL;DR: In this paper, the problem of analyzing the heterogeneity of clustering distributions for multiple groups of observed data, each of which is indexed by a covariate value, and inferring global clusters arising from observations aggregated over the covariate domain is considered.
4
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