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
3 LAGIS-SI
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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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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