Méthodes de géométrie de l'information pour les modèles de mélange

Abstract : This thesis presents new methods for mixture model learning based on information geometry. We focus on mixtures of exponential families, which encompass a large number of mixtures used in practice. With information geometry, statistical problems can be studied with geometrical tools. This framework gives new perspectives allowing to design algorithms which are both fast and generic. Two main contributions are proposed here. The first one is a method for simplification of kernel density estimators. This simplification is made with clustering algorithms, first with the Bregman divergence and next, for speed reason, with the Fisher-Rao distance and model centroids. The second contribution is a generalization of the k-MLE algorithm which allows to deal with mixtures where all the components do not belong to the same family: this method is applied to mixtures of generalized Gaussians and of Gamma laws and is faster than existing methods. The description of this two algorithms comes with a complete software implementation and their efficiency is evaluated through applications in bio-informatics and texture classification.
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Olivier Schwander. Méthodes de géométrie de l'information pour les modèles de mélange. Apprentissage [cs.LG]. Ecole Polytechnique X, 2013. Français. ⟨pastel-00931722⟩

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