The Kernel Path in Kernelized LASSO

Gang Wang, Dit-Yan Yeung, Frederick H. Lochovsky
Proceedings of the Eleventh International Conference on Artificial Intelligence and Statistics, PMLR 2:580-587, 2007.

Abstract

Kernel methods implicitly map data points from the input space to some feature space where even relatively simple algorithms such as linear methods can deliver very impressive performance. Of crucial importance though is the choice of the kernel function, which determines the mapping between the input space and the feature space. The past few years have seen many efforts in learning either the kernel function or the kernel matrix. In this paper, we study the problem of learning the kernel hyperparameter in the context of the kernelized LASSO regression model. Specifically, we propose a solution path algorithm with respect to the hyperparameter of the kernel function. As the kernel hyperparameter changes its value, the solution path can be traced exactly without having to train the model multiple times. As a result, the optimal solution can be identified efficiently. Some simulation results will be presented to demonstrate the effectiveness of our proposed kernel path algorithm.

Cite this Paper

BibTeX
@InProceedings{pmlr-v2-wang07a, title = {The Kernel Path in Kernelized LASSO}, author = {Wang, Gang and Yeung, Dit-Yan and Lochovsky, Frederick H.}, booktitle = {Proceedings of the Eleventh International Conference on Artificial Intelligence and Statistics}, pages = {580--587}, year = {2007}, editor = {Meila, Marina and Shen, Xiaotong}, volume = {2}, series = {Proceedings of Machine Learning Research}, address = {San Juan, Puerto Rico}, month = {21--24 Mar}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v2/wang07a/wang07a.pdf}, url = {https://proceedings.mlr.press/v2/wang07a.html}, abstract = {Kernel methods implicitly map data points from the input space to some feature space where even relatively simple algorithms such as linear methods can deliver very impressive performance. Of crucial importance though is the choice of the kernel function, which determines the mapping between the input space and the feature space. The past few years have seen many efforts in learning either the kernel function or the kernel matrix. In this paper, we study the problem of learning the kernel hyperparameter in the context of the kernelized LASSO regression model. Specifically, we propose a solution path algorithm with respect to the hyperparameter of the kernel function. As the kernel hyperparameter changes its value, the solution path can be traced exactly without having to train the model multiple times. As a result, the optimal solution can be identified efficiently. Some simulation results will be presented to demonstrate the effectiveness of our proposed kernel path algorithm.} }
Endnote
%0 Conference Paper %T The Kernel Path in Kernelized LASSO %A Gang Wang %A Dit-Yan Yeung %A Frederick H. Lochovsky %B Proceedings of the Eleventh International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2007 %E Marina Meila %E Xiaotong Shen %F pmlr-v2-wang07a %I PMLR %P 580--587 %U https://proceedings.mlr.press/v2/wang07a.html %V 2 %X Kernel methods implicitly map data points from the input space to some feature space where even relatively simple algorithms such as linear methods can deliver very impressive performance. Of crucial importance though is the choice of the kernel function, which determines the mapping between the input space and the feature space. The past few years have seen many efforts in learning either the kernel function or the kernel matrix. In this paper, we study the problem of learning the kernel hyperparameter in the context of the kernelized LASSO regression model. Specifically, we propose a solution path algorithm with respect to the hyperparameter of the kernel function. As the kernel hyperparameter changes its value, the solution path can be traced exactly without having to train the model multiple times. As a result, the optimal solution can be identified efficiently. Some simulation results will be presented to demonstrate the effectiveness of our proposed kernel path algorithm.
RIS
TY - CPAPER TI - The Kernel Path in Kernelized LASSO AU - Gang Wang AU - Dit-Yan Yeung AU - Frederick H. Lochovsky BT - Proceedings of the Eleventh International Conference on Artificial Intelligence and Statistics DA - 2007/03/11 ED - Marina Meila ED - Xiaotong Shen ID - pmlr-v2-wang07a PB - PMLR DP - Proceedings of Machine Learning Research VL - 2 SP - 580 EP - 587 L1 - http://proceedings.mlr.press/v2/wang07a/wang07a.pdf UR - https://proceedings.mlr.press/v2/wang07a.html AB - Kernel methods implicitly map data points from the input space to some feature space where even relatively simple algorithms such as linear methods can deliver very impressive performance. Of crucial importance though is the choice of the kernel function, which determines the mapping between the input space and the feature space. The past few years have seen many efforts in learning either the kernel function or the kernel matrix. In this paper, we study the problem of learning the kernel hyperparameter in the context of the kernelized LASSO regression model. Specifically, we propose a solution path algorithm with respect to the hyperparameter of the kernel function. As the kernel hyperparameter changes its value, the solution path can be traced exactly without having to train the model multiple times. As a result, the optimal solution can be identified efficiently. Some simulation results will be presented to demonstrate the effectiveness of our proposed kernel path algorithm. ER -
APA
Wang, G., Yeung, D. & Lochovsky, F.H.. (2007). The Kernel Path in Kernelized LASSO. Proceedings of the Eleventh International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 2:580-587 Available from https://proceedings.mlr.press/v2/wang07a.html.

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