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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 ..."
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Cited by 44 (4 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.
Minmax and minmax regret versions of combinatorial optimization problems: A survey
 European Journal of Operational Research
"... Minmax and minmax regret criteria are commonly used to define robust solutions. After motivating the use of these criteria, we present general results. Then, we survey complexity results for the minmax and minmax regret versions of some combinatorial optimization problems: shortest path, spannin ..."
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Cited by 23 (1 self)
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Minmax and minmax regret criteria are commonly used to define robust solutions. After motivating the use of these criteria, we present general results. Then, we survey complexity results for the minmax and minmax regret versions of some combinatorial optimization problems: shortest path, spanning tree, assignment, min cut, min st cut, knapsack. Since most of these problems are NPhard, we also investigate the approximability of these problems. Furthermore, we present algorithms to solve these problems to optimality.
Interdiction models and applications
 Handbook of Operations Research for Homeland Security
, 2013
"... Through interdiction models, we infer the vulnerabilities inherent in an operational system. This chapter presents four applications of interdiction modeling: (i) to delay an adversary’s development of a first nuclear weapon; (ii) to understand vulnerabilities in an electric power system; (iii) to l ..."
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Cited by 3 (0 self)
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Through interdiction models, we infer the vulnerabilities inherent in an operational system. This chapter presents four applications of interdiction modeling: (i) to delay an adversary’s development of a first nuclear weapon; (ii) to understand vulnerabilities in an electric power system; (iii) to locate sensors in a municipal water network; and (iv) to secure a border against a nuclear smuggler. In each case, we detail and interpret the mathematical model, and characterize insights gained from solving instances of the model. We point to special structures that sometimes arise in interdiction models and the associated implications for analyses. From these examples, themes emerge on how one should model, and defend against, an intelligent adversary. This chapter describes how to assess the vulnerabilities of operational systems by using interdiction models. We do so in the context of four applications from the literature: delaying an adversary’s development of a first nuclear weapon; understanding vulnerabilities in an electric power system; locating sensors to rapidly detect an illicit contaminant injected in a municipal water system; and locating radiation sensors to detect a nuclear smuggler. The key steps in this approach involve answering the following questions: (1) How is the system operated? and (2) What are the
Structural Health Monitoring Sensor Placement Optimization Under Uncertainty
"... This paper develops a methodology for the optimum layout design of sensor arrays of structural health monitoring (SHM) systems under uncertainty. This includes finite element analysis under transient mechanical and thermal loads and incorporation of uncertainty quantification methods. The finite ele ..."
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Cited by 3 (0 self)
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This paper develops a methodology for the optimum layout design of sensor arrays of structural health monitoring (SHM) systems under uncertainty. This includes finite element analysis under transient mechanical and thermal loads and incorporation of uncertainty quantification methods. The finite element model is validated with experimental data, accounting for uncertainties in experimental measurements and model predictions. The SHM sensors need to be placed optimally in order to detect with high reliability any structural damage before it turns critical. The proposed methodology achieves this objective by combining probabilistic finite element analysis, structural damage detection algorithms, and reliabilitybased optimization concepts. Nomenclature n = number of candidate sensor locations a = number of optimal sensor locations ()xf = objective function x = vector containing the coordinates of a given sensor array [u,v] = bounded box that contains all possible x (i.e. geometric constraints on x) ()CDP = probability of correct detection
Resilient Observation Selection in Adversarial Settings
"... Abstract — Monitoring large areas using sensors is fundamental in a number of applications, including electric power grid, traffic networks, and sensorbased pollution control systems. However, the number of sensors that can be deployed is often limited by financial or technological constraints. Th ..."
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Abstract — Monitoring large areas using sensors is fundamental in a number of applications, including electric power grid, traffic networks, and sensorbased pollution control systems. However, the number of sensors that can be deployed is often limited by financial or technological constraints. This problem is further complicated by the presence of strategic adversaries, who may disable some of the deployed sensors in order to impair the operator’s ability to make predictions. Assuming that the operator employs a Gaussianprocessbased regression model, we formulate the problem of attackresilient sensor placement as the problem of selecting a subset from a set of possible observations, with the goal of minimizing the uncertainty of predictions. We show that both finding an optimal resilient subset and finding an optimal attack against a given subset are NPhard problems. Since both the design and the attack problems are computationally complex, we propose efficient heuristic algorithms for solving them and present theoretical approximability results. Finally, we show that the proposed algorithms perform exceptionally well in practice using numerical results based on realworld datasets. I.
Published In Journal of Machine Learning Research, 9, 27612801. 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
 Add to MetaCart
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 pre