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Nearoptimal sensor placements: Maximizing information while minimizing communication cost
 In IPSN
, 2006
"... 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 149 (19 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 sensor locations (regardless of whether sensors were ever placed at these 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 costEffective Locations. Our approach exploits two important properties of this problem: submodularity, formalizing the intuition that adding a node to a small deployment can help more than adding a node 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 pSPIEL approach. We also provide extensive experimental validation of this practical approach on several realworld placement problems, and built a complete system implementation on 46 Tmote Sky motes, demonstrating significant advantages over existing methods.
Maximizing nonmonotone submodular functions
 In Proceedings of 48th Annual IEEE Symposium on Foundations of Computer Science (FOCS
, 2007
"... Submodular maximization generalizes many important problems including Max Cut in directed/undirected graphs and hypergraphs, certain constraint satisfaction problems and maximum facility location problems. Unlike the problem of minimizing submodular functions, the problem of maximizing submodular fu ..."
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Cited by 145 (17 self)
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Submodular maximization generalizes many important problems including Max Cut in directed/undirected graphs and hypergraphs, certain constraint satisfaction problems and maximum facility location problems. Unlike the problem of minimizing submodular functions, the problem of maximizing submodular functions is NPhard. In this paper, we design the first constantfactor approximation algorithms for maximizing nonnegative submodular functions. In particular, we give a deterministic local search 1 2approximation and a randomizedapproximation algo
Learning Influence Probabilities In Social Networks
"... Recently, there has been tremendous interest in the phenomenon of influence propagation in social networks. The studies in this area assume they have as input to their problems a social graph with edges labeled with probabilities of influence between users. However, the question of where these proba ..."
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Cited by 145 (18 self)
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Recently, there has been tremendous interest in the phenomenon of influence propagation in social networks. The studies in this area assume they have as input to their problems a social graph with edges labeled with probabilities of influence between users. However, the question of where these probabilities come from or how they can be computed from real social network data has been largely ignored until now. Thus it is interesting to ask whether from a social graph and a log of actions by its users, one can build models of influence. This is the main problem attacked in this paper. In addition to proposing models and algorithms for learning the model parameters and for testing the learned models to make predictions, we also develop techniques for predicting the time by which a user may be expected to perform an action. We validate our ideas and techniques using the Flickr data set consisting of a social graph with 1.3M nodes, 40M edges, and an action log consisting of 35M tuples referring to 300K distinct actions. Beyond showing that there is genuine influence happening in a real social network, we show that our techniques have excellent prediction performance.
Nearoptimal nonmyopic value of information in graphical models
 In Annual Conference on Uncertainty in Artificial Intelligence
"... A fundamental issue in realworld systems, such as sensor networks, is the selection of observations which most effectively reduce uncertainty. More specifically, we address the long standing problem of nonmyopically selecting the most informative subset of variables in a graphical model. We present ..."
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Cited by 142 (25 self)
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A fundamental issue in realworld systems, such as sensor networks, is the selection of observations which most effectively reduce uncertainty. More specifically, we address the long standing problem of nonmyopically selecting the most informative subset of variables in a graphical model. We present the first efficient randomized algorithm providing a constant factor (1 − 1/e − ε) approximation guarantee for any ε> 0 with high confidence. The algorithm leverages the theory of submodular functions, in combination with a polynomial bound on sample complexity. We furthermore prove that no polynomial time algorithm can provide a constant factor approximation better than (1 − 1/e) unless P = NP. Finally, we provide extensive evidence of the effectiveness of our method on two complex realworld datasets. 1
Optimal Approximation for the Submodular Welfare Problem in the value oracle model
 STOC'08
, 2008
"... In the Submodular Welfare Problem, m items are to be distributed among n players with utility functions wi: 2 [m] → R+. The utility functions are assumed to be monotone and submodular. Assuming that player i receives a set of items Si, we wish to maximize the total utility Pn i=1 wi(Si). In this pap ..."
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Cited by 122 (11 self)
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In the Submodular Welfare Problem, m items are to be distributed among n players with utility functions wi: 2 [m] → R+. The utility functions are assumed to be monotone and submodular. Assuming that player i receives a set of items Si, we wish to maximize the total utility Pn i=1 wi(Si). In this paper, we work in the value oracle model where the only access to the utility functions is through a black box returning wi(S) for a given set S. Submodular Welfare is in fact a special case of the more general problem of submodular maximization subject to a matroid constraint: max{f(S) : S ∈ I}, where f is monotone submodular and I is the collection of independent sets in some matroid. For both problems, a greedy algorithm is known to yield a 1/2approximation [21, 16]. In special cases where the matroid is uniform (I = {S: S  ≤ k}) [20] or the submodular function is of a special type [4, 2], a (1 − 1/e)approximation has been achieved and this is optimal for these problems in the value oracle model [22, 6, 15]. A (1 − 1/e)approximation for the general Submodular Welfare Problem has been known only in a stronger demand oracle model [4], where in fact 1 − 1/e can be improved [9]. In this paper, we develop a randomized continuous greedy algorithm which achieves a (1 − 1/e)approximation for the Submodular Welfare Problem in the value oracle model. We also show that the special case of n equal players is approximation resistant, in the sense that the optimal (1 − 1/e)approximation is achieved by a uniformly random solution. Using the pipage rounding technique [1, 2], we obtain a (1 − 1/e)approximation for submodular maximization subject to any matroid constraint. The continuous greedy algorithm has a potential of wider applicability, which we demonstrate on the examples of the Generalized Assignment Problem and the AdWords Assignment Problem.
Gaussian Process Optimization in the Bandit Setting: No Regret and Experimental Design
"... Many applications require optimizing an unknown, noisy function that is expensive to evaluate. We formalize this task as a multiarmed bandit problem, where the payoff function is either sampled from a Gaussian process (GP) or has low RKHS norm. We resolve the important open problem of deriving regre ..."
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Cited by 118 (11 self)
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Many applications require optimizing an unknown, noisy function that is expensive to evaluate. We formalize this task as a multiarmed bandit problem, where the payoff function is either sampled from a Gaussian process (GP) or has low RKHS norm. We resolve the important open problem of deriving regret bounds for this setting, which imply novel convergence rates for GP optimization. We analyze GPUCB, an intuitive upperconfidence based algorithm, and bound its cumulative regret in terms of maximal information gain, establishing a novel connection between GP optimization and experimental design. Moreover, by bounding the latter in terms of operator spectra, we obtain explicit sublinear regret bounds for many commonly used covariance functions. In some important cases, our bounds have surprisingly weak dependence on the dimensionality. In our experiments on real sensor data, GPUCB compares favorably with other heuristical GP optimization approaches. 1.
Maximizing a Submodular Set Function subject to a Matroid Constraint (Extended Abstract)
 PROC. OF 12 TH IPCO
, 2007
"... Let f: 2 N → R + be a nondecreasing submodular set function, and let (N, I) be a matroid. We consider the problem maxS∈I f(S). It is known that the greedy algorithm yields a 1/2approximation [9] for this problem. It is also known, via a reduction from the maxkcover problem, that there is no (1 ..."
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Cited by 114 (12 self)
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Let f: 2 N → R + be a nondecreasing submodular set function, and let (N, I) be a matroid. We consider the problem maxS∈I f(S). It is known that the greedy algorithm yields a 1/2approximation [9] for this problem. It is also known, via a reduction from the maxkcover problem, that there is no (1 − 1/e + ɛ)approximation for any constant ɛ> 0, unless P = NP [6]. In this paper, we improve the 1/2approximation to a (1−1/e)approximation, when f is a sum of weighted rank functions of matroids. This class of functions captures a number of interesting problems including set coverage type problems. Our main tools are the pipage rounding technique of Ageev and Sviridenko [1] and a probabilistic lemma on monotone submodular functions that might be of independent interest. We show that the generalized assignment problem (GAP) is a special case of our problem; although the reduction requires N  to be exponential in the original problem size, we are able to interpret the recent (1 − 1/e)approximation for GAP by Fleischer et al. [10] in our framework. This enables us to obtain a (1 − 1/e)approximation for variants of GAP with more complex constraints.
Inferring Networks of Diffusion and Influence
, 2010
"... Information diffusion and virus propagation are fundamental processes talking place in networks. While it is often possible to directly observe when nodes become infected, observing individual transmissions (i.e., who infects whom or who influences whom) is typically very difficult. Furthermore, in ..."
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Cited by 112 (13 self)
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Information diffusion and virus propagation are fundamental processes talking place in networks. While it is often possible to directly observe when nodes become infected, observing individual transmissions (i.e., who infects whom or who influences whom) is typically very difficult. Furthermore, in many applications, the underlying network over which the diffusions and propagations spread is actually unobserved. We tackle these challenges by developing a method for tracing paths of diffusion and influence through networks and inferring the networks over which contagions propagate. Given the times when nodes adopt pieces of information or become infected, we identify the optimal network that best explains the observed infection times. Since the optimization problem is NPhard to solve exactly, we develop an efficient approximation algorithm that scales to large datasets and in practice gives provably nearoptimal performance. We demonstrate the effectiveness of our approach by tracing information cascades in a set of 170 million blogs and news articles over a one year period to infer how information flows through the online media space. We find that the diffusion network of news tends to have a coreperiphery structure with a small set of core media sites that diffuse information to the rest of the Web. These sites tend to have stable circles of influence with more general news media sites acting as connectors between them.
Fast approximate energy minimization with label costs
, 2010
"... The αexpansion algorithm [7] has had a significant impact in computer vision due to its generality, effectiveness, and speed. Thus far it can only minimize energies that involve unary, pairwise, and specialized higherorder terms. Our main contribution is to extend αexpansion so that it can simult ..."
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Cited by 108 (9 self)
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The αexpansion algorithm [7] has had a significant impact in computer vision due to its generality, effectiveness, and speed. Thus far it can only minimize energies that involve unary, pairwise, and specialized higherorder terms. Our main contribution is to extend αexpansion so that it can simultaneously optimize “label costs ” as well. An energy with label costs can penalize a solution based on the set of labels that appear in it. The simplest special case is to penalize the number of labels in the solution. Our energy is quite general, and we prove optimality bounds for our algorithm. A natural application of label costs is multimodel fitting, and we demonstrate several such applications in vision: homography detection, motion segmentation, and unsupervised image segmentation. Our C++/MATLAB implementation is publicly available.