Recursive sampling for the nyström method

Cameron Musco, Christopher Musco

    Research output: Contribution to journalConference article

    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 - 2017
    Event31st Annual Conference on Neural Information Processing Systems, NIPS 2017 - Long Beach, United States
    Duration: Dec 4 2017Dec 9 2017

    ASJC Scopus subject areas

    • Computer Networks and Communications
    • Information Systems
    • Signal Processing

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  • Cite this

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