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30
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 ..."
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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.
Selecting Observations against Adversarial Objectives
, 2007
"... In many applications, one has to actively select among a set of expensive observations before making an informed decision. Often, we want to select observations which perform well when evaluated with an objective function chosen by an adversary. Examples include minimizing the maximum posterior vari ..."
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Cited by 22 (7 self)
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In many applications, one has to actively select among a set of expensive observations before making an informed decision. Often, we want to select observations which perform well when evaluated with an objective function chosen by an adversary. 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 the case 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 evaluate our algorithm 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.
Nonmyopic informative path planning in spatiotemporal models
, 2007
"... In many sensing applications we must continuously gather information to provide a good estimate of the state of the environment at every point in time. A robot may tour an environment, gathering information every hour. In a wireless sensor network, these tours correspond to packets being transmitted ..."
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Cited by 21 (8 self)
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In many sensing applications we must continuously gather information to provide a good estimate of the state of the environment at every point in time. A robot may tour an environment, gathering information every hour. In a wireless sensor network, these tours correspond to packets being transmitted. In these settings, we are often faced with resource restrictions, like energy constraints. The users issue queries with certain expectations on the answer quality. Thus, we must optimize the tours to ensure the satisfaction of the user constraints, while at the same time minimize the cost of the query plan. For a single timestep, this optimization problem is NPhard, but recent approximation algorithms with theoretical guarantees provide good solutions. In this paper, we present a new efficient algorithm, exploiting dynamic programming and submodularity of the information collected, that efficiently plans data collection tours for an entire (finite) horizon. Our algorithm can use any single step procedure as a black box, and, based on its properties, provides strong theoretical guarantees for the solution. We also provide an extensive empirical analysis demonstrating the benefits of nonmyopic planning in two real world sensing applications.
Toward Community Sensing
, 2008
"... A great opportunity exists to fuse information from populations of privatelyheld sensors to create useful sensing applications. For example, GPS devices, embedded in cellphones and automobiles, might one day be employed as distributed networks of velocity sensors for traffic monitoring and routing. ..."
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Cited by 21 (3 self)
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A great opportunity exists to fuse information from populations of privatelyheld sensors to create useful sensing applications. For example, GPS devices, embedded in cellphones and automobiles, might one day be employed as distributed networks of velocity sensors for traffic monitoring and routing. Unfortunately, privacy and resource considerations limit access to such data streams. We describe principles of community sensing that offer mechanisms for sharing data from privately held sensors. The methods take into account the likely availability of sensors, the contextsensitive value of sensor information, based on models of phenomena and demand, and sensor owners’ preferences about privacy and resource usage. We present efficient and wellcharacterized approximations of optimal sensing policies. We provide details on key principles of community sensing and highlight their use within a case study for road traffic monitoring.
Uncertaintydriven view planning for underwater inspection
 In Proc. IEEE Int. Conf. Robotics and Automation
, 2012
"... Abstract — We discuss the problem of inspecting an underwater structure, such as a submerged ship hull, with an autonomous underwater vehicle (AUV). In such scenarios, the goal is to construct an accurate 3D model of the structure and to detect any anomalies (e.g., foreign objects or deformations). ..."
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Cited by 7 (3 self)
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Abstract — We discuss the problem of inspecting an underwater structure, such as a submerged ship hull, with an autonomous underwater vehicle (AUV). In such scenarios, the goal is to construct an accurate 3D model of the structure and to detect any anomalies (e.g., foreign objects or deformations). We propose a method for constructing 3D meshes from sonarderived point clouds that provides watertight surfaces, and we introduce uncertainty modeling through nonparametric Bayesian regression. Uncertainty modeling provides novel cost functions for planning the path of the AUV to minimize a metric of inspection performance. We draw connections between the resulting cost functions and submodular optimization, which provides insight into the formal properties of active perception problems. In addition, we present experimental trials that utilize profiling sonar data from ship hull inspection. I.
Convex analysis and optimization with submodular functions: a tutorial
"... Setfunctions appear in many areas of computer science and applied mathematics, such as machine learning [1, 2, 3, 4], computer vision [5, 6], operations research [7] or electrical networks [8]. Among these setfunctions, submodular functions play an important role, similar to convex functions on ve ..."
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Cited by 7 (5 self)
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Setfunctions appear in many areas of computer science and applied mathematics, such as machine learning [1, 2, 3, 4], computer vision [5, 6], operations research [7] or electrical networks [8]. Among these setfunctions, submodular functions play an important role, similar to convex functions on vector spaces. In this tutorial, the theory of submodular
Online Distributed Sensor Selection
, 2010
"... A key problem in sensor networks is to decide which sensors to query when, in order to obtain the most useful information (e.g., for performing accurate prediction), subject to constraints (e.g., on power and bandwidth). In many applications the utility function is not known a priori, must be learne ..."
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Cited by 7 (0 self)
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A key problem in sensor networks is to decide which sensors to query when, in order to obtain the most useful information (e.g., for performing accurate prediction), subject to constraints (e.g., on power and bandwidth). In many applications the utility function is not known a priori, must be learned from data, and can even change over time. Furthermore for large sensor networks solving a centralized optimization problem to select sensors is not feasible, and thus we seek a fully distributed solution. In this paper, we present Distributed Online Greedy (DOG), an efficient, distributed algorithm for repeatedly selecting sensors online, only receiving feedback about the utility of the selected sensors. We prove very strong theoretical noregret guarantees that apply whenever the (unknown) utility function satisfies a natural diminishing returns property called submodularity. Our algorithm has extremely low communication requirements, and scales well to large sensor deployments. We extend DOG to allow observationdependent sensor selection. We empirically demonstrate the effectiveness of our algorithm on several realworld sensing tasks.
Submodular meets Spectral: Greedy Algorithms for Sparse Approximation and
 Dictonary Selection, 2011. http://arxiv.org/abs/1102.3975. Diekhoff, G. Statistics for the Social and Behavioral Sciences
"... We study the problem of selecting a subset of k random variables from a large set, in order to obtain the best linear prediction of another variable of interest. This problem can be viewed in the context of both feature selection and sparse approximation. We analyze the performance of widely used gr ..."
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Cited by 6 (0 self)
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We study the problem of selecting a subset of k random variables from a large set, in order to obtain the best linear prediction of another variable of interest. This problem can be viewed in the context of both feature selection and sparse approximation. We analyze the performance of widely used greedy heuristics, using insights from the maximization of submodular functions and spectral analysis. We introduce the submodularity ratio as a key quantity to help understand why greedy algorithms perform well even when the variables are highly correlated. Using our techniques, we obtain the strongest known approximation guarantees for this problem, both in terms of the submodularity ratio and the smallest ksparse eigenvalue of the covariance matrix. We also analyze greedy algorithms for the dictionary selection problem, and significantly improve the previously known guarantees. Our theoretical analysis is complemented by experiments on realworld and synthetic data sets; the experiments show that the submodularity ratio is a stronger predictor of the performance of greedy algorithms than other spectral parameters. 1.
Robust Sensor Placements at Informative and CommunicationEfficient Locations
, 2010
"... When monitoring spatial phenomena with wireless sensor networks, selecting the best sensor placements is a fundamental task. Not only should the sensors be informative, but they should also be able to communicate efficiently. In this paper, we present a datadriven approach that addresses the three ..."
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Cited by 3 (0 self)
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When monitoring spatial phenomena with wireless sensor networks, selecting the best sensor placements is a fundamental task. Not only should the sensors be informative, but they should also be able to communicate efficiently. In this paper, we present a datadriven approach that addresses the three central aspects of this problem: measuring the predictive quality of a set of hypothetical sensor locations, predicting the communication cost involved with these placements, and designing an algorithm with provable quality guarantees that optimizes the NPhard tradeoff. Specifically, we use data from a pilot deployment to build nonparametric probabilistic models called Gaussian Processes (GPs) both for the spatial phenomena of interest and for the spatial variability of link qualities, which allows us to estimate predictive power and communication cost of unsensed locations. Surprisingly, uncertainty in the representation of link qualities plays an important role in estimating communication costs. Using these models, we present a novel, polynomialtime, datadriven algorithm, PSPIEL, which selects Sensor Placements at Informative and communicationEfficient Locations. Our approach exploit two important properties of this problem: submodularity, formalizing the intuition that adding a node to a small deployment can help more than adding it to a large deployment; and locality, under which nodes that are far from each other provide almost independent information. Exploiting these properties, we prove strong approximation guarantees for our approach. We also show how our placements can be made robust against changes in the environment,