Subsampling in Smoothed Range Spaces
Abstract
We consider smoothed versions of geometric range spaces, so an element of the ground set (e.g. a point) can be contained in a range with a non-binary value in $[0,1]$. Similar notions have been considered for kernels; we extend them to more general types of ranges. We then consider approximations of these range spaces through $\varepsilon $-nets and $\varepsilon $-samples (aka $\varepsilon$-approximations). We characterize when size bounds for $\varepsilon $-samples on kernels can be extended to these more general smoothed range spaces. We also describe new generalizations for $\varepsilon $-nets to these range spaces and show when results from binary range spaces can carry over to these smoothed ones.
Cite
Text
Phillips and Zheng. "Subsampling in Smoothed Range Spaces." International Conference on Algorithmic Learning Theory, 2015. doi:10.1007/978-3-319-24486-0_15Markdown
[Phillips and Zheng. "Subsampling in Smoothed Range Spaces." International Conference on Algorithmic Learning Theory, 2015.](https://mlanthology.org/alt/2015/phillips2015alt-subsampling/) doi:10.1007/978-3-319-24486-0_15BibTeX
@inproceedings{phillips2015alt-subsampling,
title = {{Subsampling in Smoothed Range Spaces}},
author = {Phillips, Jeff M. and Zheng, Yan},
booktitle = {International Conference on Algorithmic Learning Theory},
year = {2015},
pages = {224-238},
doi = {10.1007/978-3-319-24486-0_15},
url = {https://mlanthology.org/alt/2015/phillips2015alt-subsampling/}
}