306 research outputs found
Lazier Than Lazy Greedy
Is it possible to maximize a monotone submodular function faster than the
widely used lazy greedy algorithm (also known as accelerated greedy), both in
theory and practice? In this paper, we develop the first linear-time algorithm
for maximizing a general monotone submodular function subject to a cardinality
constraint. We show that our randomized algorithm, STOCHASTIC-GREEDY, can
achieve a approximation guarantee, in expectation, to the
optimum solution in time linear in the size of the data and independent of the
cardinality constraint. We empirically demonstrate the effectiveness of our
algorithm on submodular functions arising in data summarization, including
training large-scale kernel methods, exemplar-based clustering, and sensor
placement. We observe that STOCHASTIC-GREEDY practically achieves the same
utility value as lazy greedy but runs much faster. More surprisingly, we
observe that in many practical scenarios STOCHASTIC-GREEDY does not evaluate
the whole fraction of data points even once and still achieves
indistinguishable results compared to lazy greedy.Comment: In Proc. Conference on Artificial Intelligence (AAAI), 201
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