233 research outputs found
Noisy Submodular Maximization via Adaptive Sampling with Applications to Crowdsourced Image Collection Summarization
We address the problem of maximizing an unknown submodular function that can
only be accessed via noisy evaluations. Our work is motivated by the task of
summarizing content, e.g., image collections, by leveraging users' feedback in
form of clicks or ratings. For summarization tasks with the goal of maximizing
coverage and diversity, submodular set functions are a natural choice. When the
underlying submodular function is unknown, users' feedback can provide noisy
evaluations of the function that we seek to maximize. We provide a generic
algorithm -- \submM{} -- for maximizing an unknown submodular function under
cardinality constraints. This algorithm makes use of a novel exploration module
-- \blbox{} -- that proposes good elements based on adaptively sampling noisy
function evaluations. \blbox{} is able to accommodate different kinds of
observation models such as value queries and pairwise comparisons. We provide
PAC-style guarantees on the quality and sampling cost of the solution obtained
by \submM{}. We demonstrate the effectiveness of our approach in an
interactive, crowdsourced image collection summarization application.Comment: Extended version of AAAI'16 pape
A Randomized Greedy Algorithm for Near-Optimal Sensor Scheduling in Large-Scale Sensor Networks
We study the problem of scheduling sensors in a resource-constrained linear
dynamical system, where the objective is to select a small subset of sensors
from a large network to perform the state estimation task. We formulate this
problem as the maximization of a monotone set function under a matroid
constraint. We propose a randomized greedy algorithm that is significantly
faster than state-of-the-art methods. By introducing the notion of curvature
which quantifies how close a function is to being submodular, we analyze the
performance of the proposed algorithm and find a bound on the expected mean
square error (MSE) of the estimator that uses the selected sensors in terms of
the optimal MSE. Moreover, we derive a probabilistic bound on the curvature for
the scenario where{\color{black}{ the measurements are i.i.d. random vectors
with bounded norm.}} Simulation results demonstrate efficacy of the
randomized greedy algorithm in a comparison with greedy and semidefinite
programming relaxation methods
A Randomized Greedy Algorithm for Near-Optimal Sensor Scheduling in Large-Scale Sensor Networks
We study the problem of scheduling sensors in a resource-constrained linear
dynamical system, where the objective is to select a small subset of sensors
from a large network to perform the state estimation task. We formulate this
problem as the maximization of a monotone set function under a matroid
constraint. We propose a randomized greedy algorithm that is significantly
faster than state-of-the-art methods. By introducing the notion of curvature
which quantifies how close a function is to being submodular, we analyze the
performance of the proposed algorithm and find a bound on the expected mean
square error (MSE) of the estimator that uses the selected sensors in terms of
the optimal MSE. Moreover, we derive a probabilistic bound on the curvature for
the scenario where{\color{black}{ the measurements are i.i.d. random vectors
with bounded norm.}} Simulation results demonstrate efficacy of the
randomized greedy algorithm in a comparison with greedy and semidefinite
programming relaxation methods
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