Learning the Kernel Function via Regularization
Abstract
We study the problem of finding an optimal kernel from a prescribed convex set of kernels K for learning a real-valued function by regularization. We establish for a wide variety of regularization functionals that this leads to a convex optimization problem and, for square loss regularization, we characterize the solution of this problem. We show that, although K may be an uncountable set, the optimal kernel is always obtained as a convex combination of at most m+2 basic kernels, where m is the number of data examples. In particular, our results apply to learning the optimal radial kernel or the optimal dot product kernel.
Cite
Text
Micchelli and Pontil. "Learning the Kernel Function via Regularization." Journal of Machine Learning Research, 2005.Markdown
[Micchelli and Pontil. "Learning the Kernel Function via Regularization." Journal of Machine Learning Research, 2005.](https://mlanthology.org/jmlr/2005/micchelli2005jmlr-learning/)BibTeX
@article{micchelli2005jmlr-learning,
title = {{Learning the Kernel Function via Regularization}},
author = {Micchelli, Charles A. and Pontil, Massimiliano},
journal = {Journal of Machine Learning Research},
year = {2005},
pages = {1099-1125},
volume = {6},
url = {https://mlanthology.org/jmlr/2005/micchelli2005jmlr-learning/}
}