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14
MAP estimation via agreement on trees: Messagepassing and linear programming
, 2002
"... We develop and analyze methods for computing provably optimal maximum a posteriori (MAP) configurations for a subclass of Markov random fields defined on graphs with cycles. By decomposing the original distribution into a convex combination of treestructured distributions, we obtain an upper bound ..."
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Cited by 191 (9 self)
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We develop and analyze methods for computing provably optimal maximum a posteriori (MAP) configurations for a subclass of Markov random fields defined on graphs with cycles. By decomposing the original distribution into a convex combination of treestructured distributions, we obtain an upper bound on the optimal value of the original problem (i.e., the log probability of the MAP assignment) in terms of the combined optimal values of the tree problems. We prove that this upper bound is tight if and only if all the tree distributions share an optimal configuration in common. An important implication is that any such shared configuration must also be a MAP configuration for the original distribution. Next we develop two approaches to attempting to obtain tight upper bounds: (a) a treerelaxed linear program (LP), which is derived from the Lagrangian dual of the upper bounds; and (b) a treereweighted maxproduct messagepassing algorithm that is related to but distinct from the maxproduct algorithm. In this way, we establish a connection between a certain LP relaxation of the modefinding problem, and a reweighted form of the maxproduct (minsum) messagepassing algorithm.
Collective classification in network data
, 2008
"... Numerous realworld applications produce networked data such as web data (hypertext documents connected via hyperlinks) and communication networks (people connected via communication links). A recent focus in machine learning research has been to extend traditional machine learning classification te ..."
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Cited by 178 (32 self)
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Numerous realworld applications produce networked data such as web data (hypertext documents connected via hyperlinks) and communication networks (people connected via communication links). A recent focus in machine learning research has been to extend traditional machine learning classification techniques to classify nodes in such data. In this report, we attempt to provide a brief introduction to this area of research and how it has progressed during the past decade. We introduce four of the most widely used inference algorithms for classifying networked data and empirically compare them on both synthetic and realworld data.
MAP estimation via agreement on (hyper)trees: Messagepassing and linear programming approaches
 IEEE Transactions on Information Theory
, 2002
"... We develop an approach for computing provably exact maximum a posteriori (MAP) configurations for a subclass of problems on graphs with cycles. By decomposing the original problem into a convex combination of treestructured problems, we obtain an upper bound on the optimal value of the original ..."
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Cited by 147 (10 self)
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We develop an approach for computing provably exact maximum a posteriori (MAP) configurations for a subclass of problems on graphs with cycles. By decomposing the original problem into a convex combination of treestructured problems, we obtain an upper bound on the optimal value of the original problem (i.e., the log probability of the MAP assignment) in terms of the combined optimal values of the tree problems. We prove that this upper bound is met with equality if and only if the tree problems share an optimal configuration in common. An important implication is that any such shared configuration must also be a MAP configuration for the original problem. Next we present and analyze two methods for attempting to obtain tight upper bounds: (a) a treereweighted messagepassing algorithm that is related to but distinct from the maxproduct (minsum) algorithm; and (b) a treerelaxed linear program (LP), which is derived from the Lagrangian dual of the upper bounds. Finally, we discuss the conditions that govern when the relaxation is tight, in which case the MAP configuration can be obtained. The analysis described here generalizes naturally to convex combinations of hypertreestructured distributions.
Distributed data association for multitarget tracking in sensor networks
 In International Conference on Information Fusion
, 2005
"... Abstract — Associating sensor measurements with target tracks is a fundamental and challenging problem in multi–target tracking. The problem is even more challenging in the context of sensor networks, since association is coupled across the network, yet centralized data processing is in general infe ..."
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Cited by 21 (2 self)
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Abstract — Associating sensor measurements with target tracks is a fundamental and challenging problem in multi–target tracking. The problem is even more challenging in the context of sensor networks, since association is coupled across the network, yet centralized data processing is in general infeasible due to power and bandwidth limitations. Hence efficient, distributed solutions are needed. We propose techniques based on graphical models to efficiently solve such data association problems in sensor networks. Our approach takes advantage of the sparsity inherent in the problem structure resulting from the fact that each target can be observed by only a small number of sensors and makes use of efficient message–passing algorithms for graphical models to infer the maximum a posteriori association configuration. We illustrate our approach for several typical scenarios in multi– target tracking. Our approach scales well with the number of sensor nodes in the network, and it is well–suited for distributed implementation. Distributed inference is realized by a message– passing algorithm which requires iterative, parallel exchange of information among neighboring nodes on the graph. So as to address trade–offs between inference performance and communication costs, we also propose a communication–sensitive form of message–passing that is capable of achieving near–optimal performance using far less communication. We demonstrate the effectiveness of our approach with experiments on simulated data. I.
Robust messagepassing for statistical inference in sensor networks
 IN: PROCEEDINGS OF THE 6TH INTERNATIONAL CONFERENCE ON INFORMATION PROCESSING IN SENSOR NETWORKS IPSN’07
, 2007
"... Largescale sensor network applications require innetwork processing and data fusion to compute statistically relevant summaries of the sensed measurements. This paper studies distributed messagepassing algorithms, in which neighboring nodes in the network pass local information relevant to a glob ..."
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Cited by 12 (1 self)
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Largescale sensor network applications require innetwork processing and data fusion to compute statistically relevant summaries of the sensed measurements. This paper studies distributed messagepassing algorithms, in which neighboring nodes in the network pass local information relevant to a global computation, for performing statistical inference. We focus on the class of reweighted belief propagation (RBP) algorithms, which includes as special cases the standard sumproduct and maxproduct algorithms for general networks with cycles, but in contrast to standard algorithms has attractive theoretical properties (uniqueness of fixed points, convergence, and robustness). Our main contribution is to design and implement a practical and modular architecture for implementing RBP algorithms in real networks. In addition, we show how intelligent scheduling of RBP messages can be used to minimize communication between motes and prolong the lifetime of the network. Our simulation and Mica2 mote deployment indicate that the proposed algorithms achieve accurate results despite realworld problems such as dying motes, dead and asymmetric links, and dropped messages. Overall, the class of RBP provides provides an ideal fit for sensor networks due to their distributed nature, requiring only local knowledge and coordination, and little requirements on other services such as reliable transmission.
Routing for statistical inference in sensor networks
 IN HANDBOOK ON ARRAY PROCESSING AND SENSOR NETWORKS, S. HAYKIN AND
, 2008
"... In the classical approach, the problem of distributed statistical inference and the problem of minimum cost routing of the measurements to the fusion center are treated separately. Such schemes cannot exploit the “inherent” saving in routing costs arising from data reduction in a sufficient statisti ..."
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Cited by 5 (5 self)
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In the classical approach, the problem of distributed statistical inference and the problem of minimum cost routing of the measurements to the fusion center are treated separately. Such schemes cannot exploit the “inherent” saving in routing costs arising from data reduction in a sufficient statistic for inference. Our approach is to conduct innetwork processing of the likelihood function which is the minimal sufficient statistic and deliver it to the fusion center for inference. We employ the Markov random field (MRF) model for spatial correlation of sensor data. The structure of the likelihood function is well known for a MRF from the famous HammersleyClifford theorem. Exploiting this structure, we show that the minimum cost routing for computation and delivery of the likelihood function is a Steiner tree on a transformed graph. This Steinertree reduction preserves the approximation ratio, which implies that any Steinertree approximation can be employed for minimum cost fusion with the same approximation ratio. In this chapter, we present an overview of this approach to minimum cost fusion.
Efficient MultiTarget Tracking Using Graphical Models
 In preparation, M.S. thesis, MIT
, 2008
"... The objective of this thesis is to develop a new framework for MultiTarget Tracking (MTT) algorithms that are distinguished by the use of statistical machine learning techniques. MTT is a crucial problem for many important practical applications such as military surveillance. Despite being a wells ..."
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Cited by 1 (0 self)
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The objective of this thesis is to develop a new framework for MultiTarget Tracking (MTT) algorithms that are distinguished by the use of statistical machine learning techniques. MTT is a crucial problem for many important practical applications such as military surveillance. Despite being a wellstudied research problem, MTT remains challenging, mostly because of the challenges of computational complexity faced by current algorithms. Taking a very different approach from any existing MTT algorithms, we use the formalism of graphical models to model the MTT problem according to its probabilistic structure, and subsequently develop efficient, approximate message passing algorithms to solve the MTT problem. Our modeling approach is able to take into account issues such as false alarms and missed detections. Although exact inference is intractable in graphs with a mix of both discrete and continuous random variables, such as the ones for MTT, our message passing algorithms utilize efficient particle
Graphical model approximations of random finite set filters,” arXiv, eprint arXiv:1105.3298
, 2011
"... Random finite sets (RFSs) has been a fruitful area of research in recent years, yielding new approximate filters such as the probability hypothesis density (PHD), cardinalised PHD (CPHD), and multiple target multiBernoulli (MeMBer). These new methods have largely been based on approximations that s ..."
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Cited by 1 (1 self)
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Random finite sets (RFSs) has been a fruitful area of research in recent years, yielding new approximate filters such as the probability hypothesis density (PHD), cardinalised PHD (CPHD), and multiple target multiBernoulli (MeMBer). These new methods have largely been based on approximations that sidestep the need for measurementtotrack association. Comparably, RFS methods that incorporate data association, such as Morelande and Challa’s (MC) method, have received little attention. This paper provides a RFS algorithm that incorporates data association similarly to the MC method, but retains computational tractability via a recently developed approximation of marginal association weights. We describe an efficient method for resolving the track coalescence phenomenon which is problematic for joint probabilistic data association (JPDA) and related methods (including MC). The method utilises a network flow optimisation, and thus is tractable for large numbers of targets. Finally, our derivation also shows that it is natural for the multitarget density to incorporate both a Poisson point process (PPP) component (representing targets that have never been detected) and a multiBernoulli component (representing targets under track). We describe a method of recycling, in which tracks with a low probability existence are transferred from the multiBernoulli component to the PPP component, effectively yielding a hybrid of MC and PHD. 1
Triangulation Based Multi Target Tracking with Mobile Sensor Networks
"... Abstract — We study the problem of designing motionplanning and sensor assignment strategies for tracking multiple targets with a mobile sensor network. We focus on triangulation based tracking where two sensors merge their measurements in order to estimate the position of a target. We present an it ..."
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Abstract — We study the problem of designing motionplanning and sensor assignment strategies for tracking multiple targets with a mobile sensor network. We focus on triangulation based tracking where two sensors merge their measurements in order to estimate the position of a target. We present an iterative and distributed algorithm for the tracking problem. An iteration starts with an initialization phase where targets are assigned to sensor pairs. Afterwards, assigned sensors relocate to improve their estimates. We refer to the problem of computing new locations for sensors (for given target assignments) as onestep tracking. After observing that onestep tracking is computationally hard, we show how it can be formulated as an energyminimization problem. This allows us to adapt wellstudied distributed algorithms for energy minimization. We present simulations to compare the performance of two such algorithms and conclude the paper with a description of the full tracking strategy. The utility of the presented strategy is demonstrated with simulations and experiments on a sensor network platform. I.