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In this paper, we develop the first one-pass streaming algorithm forsubmodular maximization that does not evaluate the entire stream even once. Bycarefully subsampling each element of data stream, our algorithm enjoys thetightest approximation guarantees in various settings while having the smallestmemory footprint and requiring the lowest number of function evaluations. Morespecifically, 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 thelargest feasible solution and $m$ is the number of matroids used to define theconstraint). For the non-monotone case, our approximation ratio increases onlyslightly to $4p+2-o(1)$. To the best or our knowledge, our algorithm is thefirst that combines the benefits of streaming and subsampling in a novel way inorder to truly scale submodular maximization to massive machine learningproblems. To showcase its practicality, we empirically evaluated theperformance of our algorithm on a video summarization application and observedthat it outperforms the state-of-the-art algorithm by up to fifty fold, whilemaintaining practically the same utility.

Do Less, Get More: Streaming Submodular Maximization with Subsampling