Nonlinear functional regression: a functional RKHS approach

Hachem Kadri, Emmanuel Duflos, Philippe Preux, Stéphane Canu, Manuel Davy
Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics, PMLR 9:374-380, 2010.

Abstract

This paper deals with functional regression, in which the input attributes as well as the response are functions. To deal with this problem, we develop a functional reproducing kernel Hilbert space approach; here, a kernel is an operator acting on a function and yielding a function. We demonstrate basic properties of these functional RKHS, as well as a representer theorem for this setting; we investigate the construction of kernels; we provide some experimental insight.

Cite this Paper

BibTeX
@InProceedings{pmlr-v9-kadri10a, title = {Nonlinear functional regression: a functional RKHS approach}, author = {Kadri, Hachem and Duflos, Emmanuel and Preux, Philippe and Canu, Stéphane and Davy, Manuel}, booktitle = {Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics}, pages = {374--380}, year = {2010}, editor = {Teh, Yee Whye and Titterington, Mike}, volume = {9}, series = {Proceedings of Machine Learning Research}, address = {Chia Laguna Resort, Sardinia, Italy}, month = {13--15 May}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v9/kadri10a/kadri10a.pdf}, url = {https://proceedings.mlr.press/v9/kadri10a.html}, abstract = {This paper deals with functional regression, in which the input attributes as well as the response are functions. To deal with this problem, we develop a functional reproducing kernel Hilbert space approach; here, a kernel is an operator acting on a function and yielding a function. We demonstrate basic properties of these functional RKHS, as well as a representer theorem for this setting; we investigate the construction of kernels; we provide some experimental insight.} }
Endnote
%0 Conference Paper %T Nonlinear functional regression: a functional RKHS approach %A Hachem Kadri %A Emmanuel Duflos %A Philippe Preux %A Stéphane Canu %A Manuel Davy %B Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2010 %E Yee Whye Teh %E Mike Titterington %F pmlr-v9-kadri10a %I PMLR %P 374--380 %U https://proceedings.mlr.press/v9/kadri10a.html %V 9 %X This paper deals with functional regression, in which the input attributes as well as the response are functions. To deal with this problem, we develop a functional reproducing kernel Hilbert space approach; here, a kernel is an operator acting on a function and yielding a function. We demonstrate basic properties of these functional RKHS, as well as a representer theorem for this setting; we investigate the construction of kernels; we provide some experimental insight.
RIS
TY - CPAPER TI - Nonlinear functional regression: a functional RKHS approach AU - Hachem Kadri AU - Emmanuel Duflos AU - Philippe Preux AU - Stéphane Canu AU - Manuel Davy BT - Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics DA - 2010/03/31 ED - Yee Whye Teh ED - Mike Titterington ID - pmlr-v9-kadri10a PB - PMLR DP - Proceedings of Machine Learning Research VL - 9 SP - 374 EP - 380 L1 - http://proceedings.mlr.press/v9/kadri10a/kadri10a.pdf UR - https://proceedings.mlr.press/v9/kadri10a.html AB - This paper deals with functional regression, in which the input attributes as well as the response are functions. To deal with this problem, we develop a functional reproducing kernel Hilbert space approach; here, a kernel is an operator acting on a function and yielding a function. We demonstrate basic properties of these functional RKHS, as well as a representer theorem for this setting; we investigate the construction of kernels; we provide some experimental insight. ER -
APA
Kadri, H., Duflos, E., Preux, P., Canu, S. & Davy, M.. (2010). Nonlinear functional regression: a functional RKHS approach. Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 9:374-380 Available from https://proceedings.mlr.press/v9/kadri10a.html.

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