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Functional Multi-Layer Perceptron: a Nonlinear Tool for Functional Data Analysis

Fabrice Rossi 1 Brieuc Conan-Guez 1
1 AxIS - Usage-centered design, analysis and improvement of information systems
CRISAM - Inria Sophia Antipolis - Méditerranée , Inria Paris-Rocquencourt
Abstract : This paper is an improved version of \cit in which we study a natural extension of Multi-Layer Perceptrons (MLP) to functional inputs. We show that fundamental results for classical MLP can be extended to functional MLP. We obtain universal approximation results that show the expressive power of functional MLP is comparable to that of numerical MLP. We obtain consistency results which imply that the estimation of optimal parameters for functional MLP is statistically well defined. We finally show on simulated and real world data that the proposed model performs in a very satisfactory way.
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https://hal.inria.fr/inria-00070768
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Submitted on : Friday, May 19, 2006 - 9:34:45 PM
Last modification on : Friday, November 13, 2020 - 2:22:05 PM
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Fabrice Rossi, Brieuc Conan-Guez. Functional Multi-Layer Perceptron: a Nonlinear Tool for Functional Data Analysis. [Research Report] RR-5228, INRIA. 2004, pp.35. ⟨inria-00070768⟩

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