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.
- Publication:
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arXiv e-prints
- Pub Date:
- October 2018
- DOI:
- 10.48550/arXiv.1810.13258
- arXiv:
- arXiv:1810.13258
- Bibcode:
- 2018arXiv181013258R
- Keywords:
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- Statistics - Machine Learning;
- Computer Science - Data Structures and Algorithms;
- Computer Science - Machine Learning