  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 Nystr\"om 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
$n^{-1/2}$ rate while reducing computational costs. We discuss applications of
this result for the approximation of the maximum mean discrepancy and
quadrature rules, and illustrate our theoretical findings with numerical
experiments.
