



@article {2376,
	title = {Sublinear quantum algorithms for training linear and kernel-based classifiers},
	journal = {Proceedings of the 36th International Conference on Machine Learning (ICML 2019) PMLR },
	volume = {97},
	year = {2019},
	month = {04/03/2019},
	pages = {3815-3824},
	abstract = {<p>We investigate quantum algorithms for classification, a fundamental problem in machine learning, with provable guarantees. Given n d-dimensional data points, the state-of-the-art (and optimal) classical algorithm for training classifiers with constant margin runs in O~(n+d) time. We design sublinear quantum algorithms for the same task running in O~(n\&minus;\&minus;\&radic;+d\&minus;\&minus;\&radic;) time, a quadratic improvement in both n and d. Moreover, our algorithms use the standard quantization of the classical input and generate the same classical output, suggesting minimal overheads when used as subroutines for end-to-end applications. We also demonstrate a tight lower bound (up to poly-log factors) and discuss the possibility of implementation on near-term quantum machines. As a side result, we also give sublinear quantum algorithms for approximating the equilibria of n-dimensional matrix zero-sum games with optimal complexity Θ~(n\&minus;\&minus;\&radic;).\&nbsp;</p>},
	url = {https://arxiv.org/abs/1904.02276},
	author = {Tongyang Li and Shouvanik Chakrabarti and Xiaodi Wu}
}
