Function Classes That Approximate the Bayes Risk
Abstract
Many learning algorithms approximately minimize a risk functional over a predefined function class. In order to establish consistency for such algorithms it is therefore necessary to know whether this function class approximates the Bayes risk. In this work we present necessary and sufficient conditions for the latter. We then apply these results to reproducing kernel Hilbert spaces used in support vector machines (SVMs). Finally, we briefly discuss universal consistency of SVMs for non-compact input domains.
Cite
Text
Steinwart et al. "Function Classes That Approximate the Bayes Risk." Annual Conference on Computational Learning Theory, 2006. doi:10.1007/11776420_9Markdown
[Steinwart et al. "Function Classes That Approximate the Bayes Risk." Annual Conference on Computational Learning Theory, 2006.](https://mlanthology.org/colt/2006/steinwart2006colt-function/) doi:10.1007/11776420_9BibTeX
@inproceedings{steinwart2006colt-function,
title = {{Function Classes That Approximate the Bayes Risk}},
author = {Steinwart, Ingo and Hush, Don R. and Scovel, Clint},
booktitle = {Annual Conference on Computational Learning Theory},
year = {2006},
pages = {79-93},
doi = {10.1007/11776420_9},
url = {https://mlanthology.org/colt/2006/steinwart2006colt-function/}
}