Institut de Mathématiques de Toulouse

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  • Mathématiques de l’apprentissage

    Mercredi 28 juin 2017 17:00-18:00 - Michal Valko - INRIA Lille - Nord Europe (Sequel)

    Distributed sequential sampling for kernel matrix approximation

    Résumé : Most kernel-based methods, such as kernel regression, kernel PCA, ICA, or k-means clustering, do not scale to large datasets, because constructing and storing the kernel matrix Kn requires at least O(n^2) time and space for n samples. Recent works (Alaoui 2014, Musco 2016) show that sampling points with replacement according to their ridge leverage scores (RLS) generates small dictionaries of relevant points with strong spectral approximation guarantees for K_n. The drawback of RLS-based methods is that computing exact RLS requires constructing and storing the whole kernel matrix. In this paper, we introduce SQUEAK, a new algorithm for kernel approximation based on RLS sampling that sequentially processes the dataset, storing a dictionary which creates accurate kernel matrix approximations with a number of points that only depends on the effective dimension d_eff(gamma) of the dataset. Moreover, since all the RLS estimations are efficiently performed using only the small dictionary, SQUEAK never constructs the whole matrix K_n, runs in linear time O(n*d_eff(gamma)^3) w.r.t. n, and requires only a single pass over the dataset. We also propose a parallel and distributed version of SQUEAK achieving similar accuracy in as little as O(log(n)*d_eff(gamma)^3) time.
    Related paper (Aistats 2017) :
    http://researchers.lille.inria.fr/ valko/hp/serve.php?what=publications/calandriello2017distributed.pdf
    This is joint work with Daniele Calandriello and Alessandro Lazaric.

    Lieu : bâtiment 1R1, salle 106

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