Séance du 15 avril 2013

Lundi 15 avril 2013

Organisateurs: Adeline Samson et Marie Luce Taupin

14h00 Estelle Kuhn (INRA)

Titre: Estimation in deformable template model in image analysis.

(joint work with Stéphanie Allassonnière and Alain Trouvé)

Résumé : We consider the framework of deformable template in image analysis and address the problem of computing an atlas of a population of images. This atlas contains some summarized information of the whole population namely a mean shape called template and the corresponding geometrical variability of the observed shapes. To tackle this issue we adopt a probabilistic point of view by considering the bayesian mixed effects template model. Our aim is to propose an accurate estimation algorithm with theoretical convergence properties and low computational cost. This becomes very demanding particular when dealing with high dimensional data. We propose to use an optimized Monte Carlo Markov Chain (MCMC) method into a stochastic Expectation Maximization(EM) algorithm in order to estimate the model parameters by maximizing likelihood. We present a new Anisotropic Metropolis Adjusted Langevin Algorithm (AMALA) which is used as transition in the MCMC method. We first prove that this new sampler leads to a geometrically uniformly ergodic Markov chain. We prove also that under mild conditions, the estimated parameter sequence converges almost surely toward a local maximum of the observed likelihood and is asymptotically Gaussian distributed. The methodology developed is then tested on handwritten digits and some medical images for the deformable model estimation. More widely, the proposed stochastic estimation algorithm can be used for a large range of models involving missing data in many fields of applications such as genetic or pharmacology.

15h00 Marie-Pierre Etienne (AgroParisTech)

Titre: Detecting genomic alteration in genomic profiles : the infinite population case.

Résumé: Two states Markov Jump process can be used to model alterations in genomic profiles along a chromosom (0 for normal state and 1 for alteration). The study of some diseases require to detect a portion of the chromosom which has been altered in a substantial fraction of patients, this leads to characterize the sojourn time above a given threshold for the process of the cumulated profiles. When the size of the population increases, we prove that the cumulated process tends to an Ornstein Uhlenbeck process. The distribution of the lengths of its excursions are not known in general and we propose a simulation

scheme to approximate the length of the largest excursion above a given threshold.

16h00 Vincent Rivoirard (Université Dauphine)

Titre : Estimation Lasso pour les processus de Hawkes multivariés.

Résumé : Motivated by statistical problems in neuroscience, we study nonparametric inference for multivariate Hawkes processes depending on an unknown function to be estimated by linear combinations of a fixed dictionary. To select coefficients, we propose a Lasso-type methodology where data-driven weights of the penalty are derived from new Bernstein type inequalities for martingales. Oracle inequalities are established under assumptions on the Gram matrix of the dictionary. Non-asymptotic probabilistic results are proven, which allows us to check these assumptions by considering general dictionaries based on histograms, Fourier or wavelet bases. We finally lead a simulation study and compare our methodology with the adaptive Lasso procedure proposed by Zou. We observe an excellent behavior of our procedure with respect to the problem of supports recovery. Unlike adaptive Lasso of Zou, our tuning procedure is proven to be robust with respect to all the parameters of the problem, revealing its potential for concrete purposes in neuroscience, but also in other fields.