Multiple Operator-valued Kernel Learning

Hachem Kadri; Alain Rakotomamonjy; Francis Bach; Philippe Preux

hal-00677012, version 2

Multiple Operator-valued Kernel Learning

Hachem Kadri (, ) ¹, Alain Rakotomamonjy () ², Francis Bach () ^3, 4, Philippe Preux ()^a^, 1

Neural Information Processing Systems (NIPS) (2012)

Abstract: Positive definite operator-valued kernels generalize the well-known notion of reproducing kernels, and are naturally adapted to multi-output learning situations. This paper addresses the problem of learning a finite linear combination of infinite-dimensional operator-valued kernels which are suitable for extending functional data analysis methods to nonlinear contexts. We study this problem in the case of kernel ridge regression for functional responses with an lr-norm constraint on the combination coefficients. The resulting optimization problem is more involved than those of multiple scalar-valued kernel learning since operator-valued kernels pose more technical and theoretical issues. We propose a multiple operator-valued kernel learning algorithm based on solving a system of linear operator equations by using a block coordinatedescent procedure. We experimentally validate our approach on a functional regression task in the context of finger movement prediction in brain-computer interfaces.

a – Université Charles de Gaulle - Lille III
1: SEQUEL (INRIA Lille - Nord Europe)
INRIA – CNRS : UMR8146 – Université Lille I - Sciences et technologies – Université Lille III - Sciences humaines et sociales – Ecole Centrale de Lille
2: Laboratoire d'Informatique, de Traitement de l'Information et des Systèmes (LITIS)
Institut National des Sciences Appliquées (INSA) - Rouen – Université du Havre – Université de Rouen : EA4108
3: SIERRA (INRIA Paris - Rocquencourt)
INRIA : PARIS - ROCQUENCOURT – Ecole normale supérieure de Paris - ENS Paris – CNRS : UMR8548
4: Laboratoire d'informatique de l'école normale supérieure (LIENS)
CNRS : UMR8548 – Ecole normale supérieure de Paris - ENS Paris

hal-00677012, version 2
http://hal.inria.fr/hal-00677012
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From: Hachem Kadri <>
Submitted on: Thursday, 14 June 2012 16:15:05
Updated on: Tuesday, 8 January 2013 11:23:32

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arXiv: 1203.1596

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%% hal-00677012, version 2
%% http://hal.inria.fr/hal-00677012
@inproceedings{kadri:hal-00677012,
    hal_id = {hal-00677012},
    url = {http://hal.inria.fr/hal-00677012},
    title = {{Multiple Operator-valued Kernel Learning}},
    author = {Kadri, Hachem and Rakotomamonjy, Alain and Bach, Francis and Preux, Philippe},
    abstract = {{Positive definite operator-valued kernels generalize the well-known notion of reproducing kernels, and are naturally adapted to multi-output learning situations. This paper addresses the problem of learning a finite linear combination of infinite-dimensional operator-valued kernels which are suitable for extending functional data analysis methods to nonlinear contexts. We study this problem in the case of kernel ridge regression for functional responses with an lr-norm constraint on the combination coefficients. The resulting optimization problem is more involved than those of multiple scalar-valued kernel learning since operator-valued kernels pose more technical and theoretical issues. We propose a multiple operator-valued kernel learning algorithm based on solving a system of linear operator equations by using a block coordinatedescent procedure. We experimentally validate our approach on a functional regression task in the context of finger movement prediction in brain-computer interfaces.}},
    keywords = {Operator-valued kernels, multiple kernel learning, nonparametric functional data analysis, function-valued reproducing kernel Hilbert spaces},
    language = {English},
    affiliation = {SEQUEL - INRIA Lille - Nord Europe , Laboratoire d'Informatique, de Traitement de l'Information et des Syst{\`e}mes - LITIS , SIERRA - INRIA Paris - Rocquencourt , Laboratoire d'informatique de l'{\'e}cole normale sup{\'e}rieure - LIENS},
    booktitle = {{Neural Information Processing Systems (NIPS)}},
    address = {Lake Tahoe, United States},
    note = {RR-7900 RR-7900 },
    audience = {international },
    year = {2012},
    month = Mar,
    pdf = {http://hal.inria.fr/hal-00677012/PDF/RR-7900.pdf},
}

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