Nyström Kernel Mean Embeddings

Antoine Chatalic · Nicolas Schreuder · Lorenzo Rosasco · Alessandro Rudi

Hall E #511

Keywords: [ PM: Monte Carlo and Sampling Methods ] [ T: Learning Theory ] [ MISC: Scalable Algorithms ] [ MISC: Unsupervised and Semi-supervised Learning ] [ MISC: Kernel methods ]


Kernel mean embeddings are a powerful tool to represent probability distributions over arbitrary spaces as single points in a Hilbert space. Yet, the cost of computing and storing such embeddings prohibits their direct use in large-scale settings. We propose an efficient approximation procedure based on the Nyström method, which exploits a small random subset of the dataset. Our main result is an upper bound on the approximation error of this procedure. It yields sufficient conditions on the subsample size to obtain the standard (1/sqrt(n)) rate while reducing computational costs. We discuss applications of this result for the approximation of the maximum mean discrepancy and quadrature rules, and we illustrate our theoretical findings with numerical experiments.

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