  In this paper, we develop the first one-pass streaming algorithm for
submodular maximization that does not evaluate the entire stream even once. By
carefully subsampling each element of data stream, our algorithm enjoys the
tightest approximation guarantees in various settings while having the smallest
memory footprint and requiring the lowest number of function evaluations. More
specifically, for a monotone submodular function and a $p$-matchoid constraint,
our randomized algorithm achieves a $4p$ approximation ratio (in expectation)
with $O(k)$ memory and $O(km/p)$ queries per element ($k$ is the size of the
largest feasible solution and $m$ is the number of matroids used to define the
constraint). For the non-monotone case, our approximation ratio increases only
slightly to $4p+2-o(1)$. To the best or our knowledge, our algorithm is the
first that combines the benefits of streaming and subsampling in a novel way in
order to truly scale submodular maximization to massive machine learning
problems. To showcase its practicality, we empirically evaluated the
performance of our algorithm on a video summarization application and observed
that it outperforms the state-of-the-art algorithm by up to fifty fold, while
maintaining practically the same utility.
