Recursive sampling for the nyström method

Cameron Musco, Christopher Musco

Research output: Contribution to journalConference article

28 Scopus citations

Abstract

We give the first algorithm for kernel Nyström approximation that runs in linear time in the number of training points and is provably accurate for all kernel matrices, without dependence on regularity or incoherence conditions. The algorithm projects the kernel onto a set of s landmark points sampled by their ridge leverage scores, requiring just O(ns) kernel evaluations and O(ns2) additional runtime. While leverage score sampling has long been known to give strong theoretical guarantees for Nyström approximation, by employing a fast recursive sampling scheme, our algorithm is the first to make the approach scalable. Empirically we show that it finds more accurate kernel approximations in less time than popular techniques such as classic Nyström approximation and the random Fourier features method.

Original languageEnglish (US)
Pages (from-to)3834-3846
Number of pages13
JournalAdvances in Neural Information Processing Systems
Volume2017-December
StatePublished - Jan 1 2017
Event31st Annual Conference on Neural Information Processing Systems, NIPS 2017 - Long Beach, United States
Duration: Dec 4 2017Dec 9 2017

All Science Journal Classification (ASJC) codes

  • Computer Networks and Communications
  • Information Systems
  • Signal Processing

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    Musco, C., & Musco, C. (2017). Recursive sampling for the nyström method. Advances in Neural Information Processing Systems, 2017-December, 3834-3846.