On Fast Leverage Score Sampling and Optimal Learning

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.

Domains

Machine Learning [cs.LG]

Fichier principal

BLESS_flattened.pdf (789.2 Ko)

imgs/HIGGSAUC.pdf (21.75 Ko)

imgs/RACCLS.pdf (39.96 Ko)

imgs/SUSYAUC.pdf (21.3 Ko)

imgs/cerr_vs_lambda.pdf (17.58 Ko)

imgs/timecomparison.pdf (19.86 Ko)

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Alessandro Rudi : Connect in order to contact the contributor

https://inria.hal.science/hal-01958879

Submitted on : Wednesday, December 19, 2018-9:10:12 AM

Last modification on : Wednesday, December 18, 2024-9:04:10 AM

Long-term archiving on : Wednesday, March 20, 2019-1:45:14 PM

Dates and versions

hal-01958879 , version 1 (19-12-2018)

Identifiers

HAL Id : hal-01958879 , version 1
ARXIV : 1810.13258

Cite

Alessandro Rudi, Daniele Calandriello, Luigi Carratino, Lorenzo Rosasco. On Fast Leverage Score Sampling and Optimal Learning. NeurIPS 2018 - Thirty-second Conference on Neural Information Processing Systems, Dec 2018, Montreal, Canada. pp.5677--5687. ⟨hal-01958879⟩

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