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Operator-Valued Kernels for Nonparametric Operator Estimation

Hachem Kadri 1, 2 Philippe Preux 1 Emmanuel Duflos 1, 3 Stephane Canu 4
1 SEQUEL - Sequential Learning
LIFL - Laboratoire d'Informatique Fondamentale de Lille, Inria Lille - Nord Europe, LAGIS - Laboratoire d'Automatique, Génie Informatique et Signal
LAGIS - Laboratoire d'Automatique, Génie Informatique et Signal
Abstract : We consider the supervised learning problem when both covariates and responses are real functions rather than scalars or finite dimensional vectors. In this setting, we aim at developing a sound and effective nonparametric operator estimation approach based on optimal approximation in reproducing kernel Hilbert spaces of function-valued functions. In a first step, we exhibit a class of operator-valued kernels that perform the mapping between two spaces of functions: this is the first contribution of this paper. Then, we show how to solve the problem of minimizing a regularized functional without discretizing covariate and target functions. Finally, we apply this framework to a standard functional regression problem.
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Submitted on : Thursday, April 21, 2011 - 5:08:30 PM
Last modification on : Saturday, December 18, 2021 - 3:05:00 AM
Long-term archiving on: : Friday, July 22, 2011 - 2:42:14 AM


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  • HAL Id : inria-00587649, version 1


Hachem Kadri, Philippe Preux, Emmanuel Duflos, Stephane Canu. Operator-Valued Kernels for Nonparametric Operator Estimation. [Research Report] RR-7607, INRIA. 2011. ⟨inria-00587649⟩



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