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Modélisation supervisée de données fonctionnelles par perceptron multi-couches

Brieuc Conan-Guez 1
1 AxIS - Usage-centered design, analysis and improvement of information systems
CRISAM - Inria Sophia Antipolis - Méditerranée , Inria Paris-Rocquencourt
Abstract : Functional Data Analysis is an extension of traditional data analysis to individuals described by functions. In this work, we present an adaptation of Multi-Layer Perceptron to functional spaces. Two approaches are proposed : a direct approach which relies on the direct manipulation of input functions, and a projection based approach, which represents input functions thanks to projection on a truncated base. For both approaches, we show that the proposed models have the universal approximation property, moreover parameter estimation is consistent when input functions are described by a finite number of input/output pairs (such as (x,g(x))). It is worth noticing that this result relies on a probabilistic modelling of function design. At last, we show that this model can be adapted in order to have a functional response, this extension allows treatment of functional discret-time processes.
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Brieuc Conan-Guez. Modélisation supervisée de données fonctionnelles par perceptron multi-couches. Mathématiques [math]. Université Paris Dauphine - Paris IX, 2002. Français. ⟨tel-00178892⟩

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