Kernels for Vector-Valued Functions: a Review

Mauricio A. ÁlvarezLorenzo RosascoNeil D. Lawrence
, 2011.

Abstract

Kernel methods are among the most popular techniques in machine learning. From a frequentist/discriminative perspective they play a central role in regularization theory as they provide a natural choice for the hypotheses space and the regularization functional through the notion of reproducing kernel Hilbert spaces. From a Bayesian/generative perspective they are the key in the context of Gaussian processes, where the kernel function is also known as the covariance function. Traditionally, kernel methods have been used in supervised learning problem with scalar outputs and indeed there has been a considerable amount of work devoted to designing and learning kernels. More recently there has been an increasing interest in methods that deal with multiple outputs, motivated partly by frameworks like multitask learning. In this paper, we review different methods to design or learn valid kernel functions for multiple outputs, paying particular attention to the connection between probabilistic and functional methods.

Cite this Paper


BibTeX
@InProceedings{pmlr-v-alvarez-kernels11, title = {Kernels for Vector-Valued Functions: a Review}, author = {Mauricio A. Álvarez and Lorenzo Rosasco and Neil D. Lawrence}, year = {}, editor = {}, url = {http://inverseprobability.com/publications/alvarez-kernels11.html}, abstract = {Kernel methods are among the most popular techniques in machine learning. From a frequentist/discriminative perspective they play a central role in regularization theory as they provide a natural choice for the hypotheses space and the regularization functional through the notion of reproducing kernel Hilbert spaces. From a Bayesian/generative perspective they are the key in the context of Gaussian processes, where the kernel function is also known as the covariance function. Traditionally, kernel methods have been used in supervised learning problem with scalar outputs and indeed there has been a considerable amount of work devoted to designing and learning kernels. More recently there has been an increasing interest in methods that deal with multiple outputs, motivated partly by frameworks like multitask learning. In this paper, we review different methods to design or learn valid kernel functions for multiple outputs, paying particular attention to the connection between probabilistic and functional methods.} }
Endnote
%0 Conference Paper %T Kernels for Vector-Valued Functions: a Review %A Mauricio A. Álvarez %A Lorenzo Rosasco %A Neil D. Lawrence %B %C Proceedings of Machine Learning Research %D %E %F pmlr-v-alvarez-kernels11 %I PMLR %J Proceedings of Machine Learning Research %P -- %U http://inverseprobability.com %V %W PMLR %X Kernel methods are among the most popular techniques in machine learning. From a frequentist/discriminative perspective they play a central role in regularization theory as they provide a natural choice for the hypotheses space and the regularization functional through the notion of reproducing kernel Hilbert spaces. From a Bayesian/generative perspective they are the key in the context of Gaussian processes, where the kernel function is also known as the covariance function. Traditionally, kernel methods have been used in supervised learning problem with scalar outputs and indeed there has been a considerable amount of work devoted to designing and learning kernels. More recently there has been an increasing interest in methods that deal with multiple outputs, motivated partly by frameworks like multitask learning. In this paper, we review different methods to design or learn valid kernel functions for multiple outputs, paying particular attention to the connection between probabilistic and functional methods.
RIS
TY - CPAPER TI - Kernels for Vector-Valued Functions: a Review AU - Mauricio A. Álvarez AU - Lorenzo Rosasco AU - Neil D. Lawrence BT - PY - DA - ED - ID - pmlr-v-alvarez-kernels11 PB - PMLR SP - DP - PMLR EP - L1 - UR - http://inverseprobability.com/publications/alvarez-kernels11.html AB - Kernel methods are among the most popular techniques in machine learning. From a frequentist/discriminative perspective they play a central role in regularization theory as they provide a natural choice for the hypotheses space and the regularization functional through the notion of reproducing kernel Hilbert spaces. From a Bayesian/generative perspective they are the key in the context of Gaussian processes, where the kernel function is also known as the covariance function. Traditionally, kernel methods have been used in supervised learning problem with scalar outputs and indeed there has been a considerable amount of work devoted to designing and learning kernels. More recently there has been an increasing interest in methods that deal with multiple outputs, motivated partly by frameworks like multitask learning. In this paper, we review different methods to design or learn valid kernel functions for multiple outputs, paying particular attention to the connection between probabilistic and functional methods. ER -
APA
Álvarez, M.A., Rosasco, L. & Lawrence, N.D.. (). Kernels for Vector-Valued Functions: a Review. , in PMLR :-

Related Material