On Fast Leverage Score Sampling and Optimal Learning
Abstract
Leverage score sampling provides an appealing way to perform approximate computations for large matrices. Indeed, it allows to derive faithful approximations with a complexity adapted to the problem at hand. Yet, performing leverage scores sampling is a challenge in its own right requiring further approximations. In this paper, we study the problem of leverage score sampling for positive definite matrices defined by a kernel. Our contribution is twofold. First we provide a novel algorithm for leverage score sampling and second, we exploit the proposed method in statistical learning by deriving a novel solver for kernel ridge regression. Our main technical contribution is showing that the proposed algorithms are currently the most efficient and accurate for these problems.
Cite
@article{arxiv.1810.13258,
title = {On Fast Leverage Score Sampling and Optimal Learning},
author = {Alessandro Rudi and Daniele Calandriello and Luigi Carratino and Lorenzo Rosasco},
journal= {arXiv preprint arXiv:1810.13258},
year = {2019}
}