Institut de Mathématiques de Toulouse

Les événements de la journée


3 événements


  • Géométrie complexe

    Jeudi 14 mars 10:30-11:30 - Andrea Fanelli - Université de Versailles St Quentin

    Simple connexité rationnelle pour les variétés de Fano : quelques exemples.

    Résumé : Même si la notion précise de variété rationnellement simplement connexe n’est pas encore claire en général, le travail de de Jong-Starr et de Jong-He-Starr a déjà suscité plusieurs études récentes pour approfondir cette notion. Dans un projet avec Laurent Gruson et Nicolas Perrin, nous étudions la simple connexité rationnelle pour des exemples de variétés de Fano en petite dimension par des méthodes explicites de géométrie birationnelle.

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  • Séminaire Mathématiques pour la biologie

    Jeudi 14 mars 13:30-14:30 - Alexandra Lefebvre - Université de la Sorbonne

    A sum-product algorithm with polynomials for computing exact derivatives of the likelihood in Bayesian networks and Hidden Markov Models. Applications to genetic linkage analysis and the local score of a sequence.

    Résumé : We consider a Bayesian network over n variables with a parameter theta. The probability of an evidence (a set of given values) can be computed through the sum of products of potentials (Koller, 2009) where the potentials are conditional probabilities for values in the evidence and zero otherwise. From a statistical point of view, the probability of the evidence conditional on theta is the likelihood of theta. Computing the derivatives of the likelihood function is of great interest, especially the first and second order derivatives from which one can derive the score and the observed Fisher information matrix. These quantities can not only help maximizing the likelihood function (e.g. through Newton-based algorithms) but also allow to obtain confidence intervals on parameters as well as performing hypothesis testing (likelihood ratio tests, score tests and Wald tests). Polynomial versions of the sum-product algorithm can be very efficient for performing complex computations in probabilistic graphical models (e.g. order k moment of an additive functional in Bayesian networks (Cowell, 1992 ; Nilsson, 2001), moment/probability generating functions in pattern matching (Nuel, 2010). In the present work we want to take advantage of polynomial arithmetic for simplified computations through a single sum-product recursion to compute both the likelihood function and all its derivatives. For a unidimensional parameter, our method allows one to compute the derivatives up order d with a complexity of O(C d^2) where C is the complexity for computing the likelihood through the original sum-product recursion. For a multidimensional parameter (p dimensions) we obtain the likelihood, the gradient and the Hessian with a complexity of O(C p^2). We illustrate our new method with to examples : the two-point linkage analysis model which is used in genetics for localizing a gene of interest and the estimation of scoring functions for the local score of one sequence.

    Lieu : salle MIP, 1er étage bat 1R3

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  • Séminaire Maths-Physique IMT-LPT

    Jeudi 14 mars 14:00-15:30 - Pierre Pujol - LPT (Toulouse)

    TBA

    Résumé : TBA

    Lieu : Salle 106, Bâtiment 1R1

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