On Fast Leverage Score Sampling and Optimal Learning

Part of Advances in Neural Information Processing Systems 31 (NeurIPS 2018)

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Alessandro Rudi, Daniele Calandriello, Luigi Carratino, Lorenzo Rosasco


Leverage score sampling provides an appealing way to perform approximate com- putations 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 ma- trices 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.