  The sheer scale of modern datasets has resulted in a dire need for
summarization techniques that identify representative elements in a dataset.
Fortunately, the vast majority of data summarization tasks satisfy an intuitive
diminishing returns condition known as submodularity, which allows us to find
nearly-optimal solutions in linear time. We focus on a two-stage submodular
framework where the goal is to use some given training functions to reduce the
ground set so that optimizing new functions (drawn from the same distribution)
over the reduced set provides almost as much value as optimizing them over the
entire ground set. In this paper, we develop the first streaming and
distributed solutions to this problem. In addition to providing strong
theoretical guarantees, we demonstrate both the utility and efficiency of our
algorithms on real-world tasks including image summarization and ride-share
optimization.
