How SVMs Can Estimate Quantiles and the Median
Abstract
We investigate quantile regression based on the pinball loss and the ǫ-insensitive loss. For the pinball loss a condition on the data-generating distribution P is given that ensures that the conditional quantiles are approximated with respect to k · k1. This result is then used to derive an oracle inequality for an SVM based on the pinball loss. Moreover, we show that SVMs based on the ǫ-insensitive loss estimate the conditional median only under certain conditions on P .
Cite
Text
Christmann and Steinwart. "How SVMs Can Estimate Quantiles and the Median." Neural Information Processing Systems, 2007.Markdown
[Christmann and Steinwart. "How SVMs Can Estimate Quantiles and the Median." Neural Information Processing Systems, 2007.](https://mlanthology.org/neurips/2007/christmann2007neurips-svms/)BibTeX
@inproceedings{christmann2007neurips-svms,
title = {{How SVMs Can Estimate Quantiles and the Median}},
author = {Christmann, Andreas and Steinwart, Ingo},
booktitle = {Neural Information Processing Systems},
year = {2007},
pages = {305-312},
url = {https://mlanthology.org/neurips/2007/christmann2007neurips-svms/}
}