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Robust submodular observation selection
, 2008
"... In many applications, one has to actively select among a set of expensive observations before making an informed decision. For example, in environmental monitoring, we want to select locations to measure in order to most effectively predict spatial phenomena. Often, we want to select observations wh ..."
Abstract

Cited by 30 (3 self)
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In many applications, one has to actively select among a set of expensive observations before making an informed decision. For example, in environmental monitoring, we want to select locations to measure in order to most effectively predict spatial phenomena. Often, we want to select observations which are robust against a number of possible objective functions. Examples include minimizing the maximum posterior variance in Gaussian Process regression, robust experimental design, and sensor placement for outbreak detection. In this paper, we present the Submodular Saturation algorithm, a simple and efficient algorithm with strong theoretical approximation guarantees for cases where the possible objective functions exhibit submodularity, an intuitive diminishing returns property. Moreover, we prove that better approximation algorithms do not exist unless NPcomplete problems admit efficient algorithms. We show how our algorithm can be extended to handle complex cost functions (incorporating nonunit observation cost or communication and path costs). We also show how the algorithm can be used to nearoptimally trade off expectedcase (e.g., the Mean Square Prediction Error in Gaussian Process regression) and worstcase (e.g., maximum predictive variance) performance. We show that many important machine learning problems fit our robust submodular observation selection formalism, and provide extensive empirical evaluation on several realworld problems. For Gaussian Process regression, our algorithm compares favorably with stateoftheart heuristics described in the geostatistics literature, while being simpler, faster and providing theoretical guarantees. For robust experimental design, our algorithm performs favorably compared to SDPbased algorithms.