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Séminaire du jeudi 19/04/2012

Jeudi, Avril 19, 2012 - 14:00 to 16:00
Bat A10, Salle: ALC

Orateur : Eric Thiébaut
Affiliation : CRAL / Observatoire de Lyon
Titre : Mise en œuvre de l'approche inverse pour la reconstruction et la détection en astronomie et en imagerie bio-médicale.
Résumé : L'approche inverse est une méthode de traitement du signal qui vise à retrouver une description de l'objet d'intérêt étant donné des mesures et un modèle du système d'observation. À travers quelques exemples, je montrerai comment nous avons exploité cette approche pour résoudre des problèmes de reconstruction d'image et de détection en astronomie. Les méthodes développées étant très générales nous les avons appliquées à d'autres domaines comme l'imagerie bio-médicale et l'holographie numérique.

Orateur : François Caron
Affiliation : INRIA, Bordeaux
Titre : Hierarchical models for constructing sparsity-inducing priors. Application to the analysis of genetic association signals
Résumé : Variable selection techniques have become increasingly popular amongst statisticians due to an increased number of regression and classification applications involving highdimensional data where we expect some predictors to be unimportant. We explore here the use of generalized t priors on regression coefficients to help understand the nature of association signal within "hit regions" of genome-wide association studies. For low degrees of freedom we show that the generalized t exhibits 'sparsity-prior' properties with some attractive features over other common forms of sparse priors and includes the well known double-exponential distribution as the degrees of freedom tends to infinity.

I will first present a scale-mixture representation of the generalized t prior that leads to an EM algorithm to obtain MAP estimates should only these be required.

Then I will look at a fully Bayesian analysis of the problem. We pay particular attention to graphical representations of posterior statistics obtained from sparsity-path-analysis (SPA) where we sweep over the setting of the scale (shrinkage / precision) parameter in the prior to explore the space of posterior models obtained over a range of complexities, from very sparse models with all coefficient distributions heavily concentrated around zero, to models with diffuse priors and coefficients distributed around their maximum likelihood estimates. The SPA plots are akin to LASSO plots of maximum a posteriori (MAP) estimates but they characterise the complete marginal posterior distributions of the coefficients plotted as a function of the precision of the prior. Generating posterior distributions over a range of prior precisions is computationally challenging but naturally amenable to sequential Monte Carlo (SMC) algorithms indexed on the scale parameter. We show how SMC simulation on graphic-processing-units (GPUs) provides very efficient inference for SPA.