Stability of Multi-Task Kernel Regression Algorithms

Julien Audiffren, Hachem Kadri
Proceedings of the 5th Asian Conference on Machine Learning, PMLR 29:1-16, 2013.

Abstract

We study the stability properties of nonlinear multi-task regression in reproducing Hilbert spaces with operator-valued kernels. Such kernels, a.k.a. multi-task kernels, are appropriate for learning problems with nonscalar outputs like multi-task learning and structured output prediction. We show that multi-task kernel regression algorithms are uniformly stable in the general case of infinite-dimensional output spaces. We then derive under mild assumption on the kernel generalization bounds of such algorithms, and we show their consistency even with non Hilbert-Schmidt operator-valued kernels. We demonstrate how to apply the results to various multi-task kernel regression methods such as vector-valued SVR and functional ridge regression.

Cite this Paper

BibTeX
@InProceedings{pmlr-v29-Audiffren13, title = {Stability of Multi-Task Kernel Regression Algorithms}, author = {Audiffren, Julien and Kadri, Hachem}, booktitle = {Proceedings of the 5th Asian Conference on Machine Learning}, pages = {1--16}, year = {2013}, editor = {Ong, Cheng Soon and Ho, Tu Bao}, volume = {29}, series = {Proceedings of Machine Learning Research}, address = {Australian National University, Canberra, Australia}, month = {13--15 Nov}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v29/Audiffren13.pdf}, url = {https://proceedings.mlr.press/v29/Audiffren13.html}, abstract = {We study the stability properties of nonlinear multi-task regression in reproducing Hilbert spaces with operator-valued kernels. Such kernels, a.k.a. multi-task kernels, are appropriate for learning problems with nonscalar outputs like multi-task learning and structured output prediction. We show that multi-task kernel regression algorithms are uniformly stable in the general case of infinite-dimensional output spaces. We then derive under mild assumption on the kernel generalization bounds of such algorithms, and we show their consistency even with non Hilbert-Schmidt operator-valued kernels. We demonstrate how to apply the results to various multi-task kernel regression methods such as vector-valued SVR and functional ridge regression.} }
Endnote
%0 Conference Paper %T Stability of Multi-Task Kernel Regression Algorithms %A Julien Audiffren %A Hachem Kadri %B Proceedings of the 5th Asian Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2013 %E Cheng Soon Ong %E Tu Bao Ho %F pmlr-v29-Audiffren13 %I PMLR %P 1--16 %U https://proceedings.mlr.press/v29/Audiffren13.html %V 29 %X We study the stability properties of nonlinear multi-task regression in reproducing Hilbert spaces with operator-valued kernels. Such kernels, a.k.a. multi-task kernels, are appropriate for learning problems with nonscalar outputs like multi-task learning and structured output prediction. We show that multi-task kernel regression algorithms are uniformly stable in the general case of infinite-dimensional output spaces. We then derive under mild assumption on the kernel generalization bounds of such algorithms, and we show their consistency even with non Hilbert-Schmidt operator-valued kernels. We demonstrate how to apply the results to various multi-task kernel regression methods such as vector-valued SVR and functional ridge regression.
RIS
TY - CPAPER TI - Stability of Multi-Task Kernel Regression Algorithms AU - Julien Audiffren AU - Hachem Kadri BT - Proceedings of the 5th Asian Conference on Machine Learning DA - 2013/10/21 ED - Cheng Soon Ong ED - Tu Bao Ho ID - pmlr-v29-Audiffren13 PB - PMLR DP - Proceedings of Machine Learning Research VL - 29 SP - 1 EP - 16 L1 - http://proceedings.mlr.press/v29/Audiffren13.pdf UR - https://proceedings.mlr.press/v29/Audiffren13.html AB - We study the stability properties of nonlinear multi-task regression in reproducing Hilbert spaces with operator-valued kernels. Such kernels, a.k.a. multi-task kernels, are appropriate for learning problems with nonscalar outputs like multi-task learning and structured output prediction. We show that multi-task kernel regression algorithms are uniformly stable in the general case of infinite-dimensional output spaces. We then derive under mild assumption on the kernel generalization bounds of such algorithms, and we show their consistency even with non Hilbert-Schmidt operator-valued kernels. We demonstrate how to apply the results to various multi-task kernel regression methods such as vector-valued SVR and functional ridge regression. ER -
APA
Audiffren, J. & Kadri, H.. (2013). Stability of Multi-Task Kernel Regression Algorithms. Proceedings of the 5th Asian Conference on Machine Learning, in Proceedings of Machine Learning Research 29:1-16 Available from https://proceedings.mlr.press/v29/Audiffren13.html.

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