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Séminaire du vendredi 21/12/2012

Vendredi, Décembre 21, 2012 - 14:00 to 16:00
IMB, Bat A33, Salle de conférence


Orateur : Nicolas Dobigeon

Affiliation : Université de Toulouse, IRIT / INP-ENSEEIHT

Titre : Bayesian approaches for subspace estimation

Résumé : In this talk, we will consider the problem of estimating a lower-dimensional subspace in a Bayesian setting. This problem can be formulated as the estimation of the semi-orthogonal matrix H whose columns span the subspace to be recoverd. Since the mean square error between the true subspace and its estimate is not the natural metric on the Grassmann manifold, we propose to carry out subspace estimation by minimizing a mean square distance, where the considered distance is a more natural metric defined on this manifold. The resulting estimator is no longer the posterior mean of H, but relies on the principal eigenvectors of the posterior mean of the associated projection matrix HH^T. Several prior models will be investigated and the resulting estimators are derived analytically or approximated by Monte Carlo sampling. An application to hyperspectral imagery will be discussed.


Orateur : Alfred Hero

Affiliation : University of Michigan

Titre : Prediction of correlation structure from large random matrices

Résumé : Random matrices arise in many areas of engineering, social sciences, and natural sciences. For example, when rows of the random matrix record successive samples of a multivariate response the sample correlation between the columns can reveal important dependency structure in the multivariate response, e.g., stars, hubs and triangles of co-dependency. However, when the number of samples is finite and the number p of columns increases such exploration becomes futile due to a phase transition phenomenon: spurious discoveries will eventually dominate. In this presentation I will present theory for predicting these phase transitions and present Poisson limit theorems that can be used to predict finite sample behavior of correlation structure. We will discuss an application to longitudinal gene expression analysis.