General Framework for Nonlinear Functional Regression with Reproducing Kernel Hilbert Spaces

Hachem Kadri 1 Emmanuel Duflos 1 Manuel Davy 1 Philippe Preux 1 Stephane Canu 2
1 SEQUEL - Sequential Learning
LIFL - Laboratoire d'Informatique Fondamentale de Lille, Inria Lille - Nord Europe, LAGIS - Laboratoire d'Automatique, Génie Informatique et Signal
Abstract : In this paper, we discuss concepts and methods of nonlinear regression for functional data. The focus is on the case where covariates and responses are functions. We present a general framework for modelling functional regression problem in the Reproducing Kernel Hilbert Space (RKHS). Basics concepts of kernel regression analysis in the real case are extended to the domain of functional data analysis. Our main results show how using Hilbert spaces theory to estimate a regression function from observed functional data. This procedure can be thought of as a generalization of scalar-valued nonlinear regression estimate.
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Hachem Kadri, Emmanuel Duflos, Manuel Davy, Philippe Preux, Stephane Canu. General Framework for Nonlinear Functional Regression with Reproducing Kernel Hilbert Spaces. [Research Report] RR-6908, INRIA. 2009. ⟨inria-00378381⟩

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