164 research outputs found
Diverse Weighted Bipartite b-Matching
Bipartite matching, where agents on one side of a market are matched to
agents or items on the other, is a classical problem in computer science and
economics, with widespread application in healthcare, education, advertising,
and general resource allocation. A practitioner's goal is typically to maximize
a matching market's economic efficiency, possibly subject to some fairness
requirements that promote equal access to resources. A natural balancing act
exists between fairness and efficiency in matching markets, and has been the
subject of much research.
In this paper, we study a complementary goal---balancing diversity and
efficiency---in a generalization of bipartite matching where agents on one side
of the market can be matched to sets of agents on the other. Adapting a
classical definition of the diversity of a set, we propose a quadratic
programming-based approach to solving a supermodular minimization problem that
balances diversity and total weight of the solution. We also provide a scalable
greedy algorithm with theoretical performance bounds. We then define the price
of diversity, a measure of the efficiency loss due to enforcing diversity, and
give a worst-case theoretical bound. Finally, we demonstrate the efficacy of
our methods on three real-world datasets, and show that the price of diversity
is not bad in practice
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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