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Pénalités hiérarchiques pour l'intégration de connaissances dans les modèles statistiques

Abstract : Supervised learning aims at predicting, but also analyzing or interpreting an observed phenomenon. Hierarchical penalization is a generic framework for integrating prior information in the fitting of statistical models. This prior information represents the relations shared by the characteristics of a given studied problem. In this thesis, the characteristics are organized in a two-levels tree structure, which defines distinct groups. The assumption is that few (groups of) characteristics are involved to discriminate between observations. Thus, for a learning problem, the goal is to identify relevant groups of characteristics, and at the same time, the significant characteristics within these groups. An adaptive penalization formulation is used to extract the significant components of each level. We show that the solution of this problem is equivalent to minimize a problem regularized by a mixed norm. These two approaches have been used to study the convexity and sparseness properties of the method. The latter is derived in parametric and non parametric function spaces. Experiences on brain-computer interfaces problems support our approach.
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https://tel.archives-ouvertes.fr/tel-00369025
Contributor : Marie Szafranski <>
Submitted on : Tuesday, June 22, 2010 - 12:41:44 AM
Last modification on : Friday, October 23, 2020 - 4:40:56 PM
Long-term archiving on: : Thursday, September 23, 2010 - 12:46:18 PM

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  • HAL Id : tel-00369025, version 2

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Marie Szafranski. Pénalités hiérarchiques pour l'intégration de connaissances dans les modèles statistiques. Autre [cs.OH]. Université de Technologie de Compiègne, 2008. Français. ⟨tel-00369025v2⟩

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