Learning Sparse Low-Threshold Linear Classifiers
Abstract
We consider the problem of learning a non-negative linear classifier with a $\ell_1$-norm of at most $k$, and a fixed threshold, under the hinge-loss. This problem generalizes the problem of learning a $k$-monotone disjunction. We prove that we can learn efficiently in this setting, at a rate which is linear in both $k$ and the size of the threshold, and that this is the best possible rate. We provide an efficient online learning algorithm that achieves the optimal rate, and show that in the batch case, empirical risk minimization achieves this rate as well. The rates we show are tighter than the uniform convergence rate, which grows with $k^2$.
Cite
Text
Sabato et al. "Learning Sparse Low-Threshold Linear Classifiers." Journal of Machine Learning Research, 2015.Markdown
[Sabato et al. "Learning Sparse Low-Threshold Linear Classifiers." Journal of Machine Learning Research, 2015.](https://mlanthology.org/jmlr/2015/sabato2015jmlr-learning/)BibTeX
@article{sabato2015jmlr-learning,
title = {{Learning Sparse Low-Threshold Linear Classifiers}},
author = {Sabato, Sivan and Shalev-Shwartz, Shai and Srebro, Nathan and Hsu, Daniel and Zhang, Tong},
journal = {Journal of Machine Learning Research},
year = {2015},
pages = {1275-1304},
volume = {16},
url = {https://mlanthology.org/jmlr/2015/sabato2015jmlr-learning/}
}