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44
Loopy belief propagation: Convergence and effects of message errors
 Journal of Machine Learning Research
, 2005
"... Belief propagation (BP) is an increasingly popular method of performing approximate inference on arbitrary graphical models. At times, even further approximations are required, whether due to quantization of the messages or model parameters, from other simplified message or model representations, or ..."
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Cited by 104 (9 self)
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Belief propagation (BP) is an increasingly popular method of performing approximate inference on arbitrary graphical models. At times, even further approximations are required, whether due to quantization of the messages or model parameters, from other simplified message or model representations, or from stochastic approximation methods. The introduction of such errors into the BP message computations has the potential to affect the solution obtained adversely. We analyze the effect resulting from message approximation under two particular measures of error, and show bounds on the accumulation of errors in the system. This analysis leads to convergence conditions for traditional BP message passing, and both strict bounds and estimates of the resulting error in systems of approximate BP message passing. 1
Using Probabilistic Models for Data Management in Acquisitional Environments
, 2005
"... Traditional database systems, particularly those focused on capturing and managing data from the real world, are poorly equipped to deal with the noise, loss, and uncertainty in data. We discuss a suite of techniques based on probabilistic models that are designed to allow database to tolerate noise ..."
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Cited by 56 (3 self)
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Traditional database systems, particularly those focused on capturing and managing data from the real world, are poorly equipped to deal with the noise, loss, and uncertainty in data. We discuss a suite of techniques based on probabilistic models that are designed to allow database to tolerate noise and loss. These techniques are based on exploiting correlations to predict missing values and identify outliers. Interestingly, correlations also provide a way to give approximate answers to users at a significantly lower cost and enable a range of new types of queries over the correlation structure itself. We illustrate a host of applications for our new techniques and queries, ranging from sensor networks to network monitoring to data stream management. We also present a unified architecture for integrating such models into database systems, focusing in particular on acquisitional systems where the cost of capturing data (e.g., from sensors) is itself a significant part of the query processing cost.
Modelbased Approximate Querying in Sensor Networks
 VLDB JOURNAL
, 2005
"... Declarative queries are proving to be an attractive paradigm for interacting with networks of wireless sensors. The metaphor that “the sensornet is a database” is problematic, however, because sensors do not exhaustively represent the data in the real world. In order to map the raw sensor readings ..."
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Cited by 51 (0 self)
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Declarative queries are proving to be an attractive paradigm for interacting with networks of wireless sensors. The metaphor that “the sensornet is a database” is problematic, however, because sensors do not exhaustively represent the data in the real world. In order to map the raw sensor readings onto physical reality, a model of that reality is required to complement the readings. In this article, we enrich interactive sensor querying with statistical modeling techniques. We demonstrate that such models can help provide answers that are both more meaningful, and, by introducing approximations with probabilistic confidences, significantly more efficient to compute in both time and energy. Utilizing the combination of a model and live data acquisition raises the challenging optimization problem of selecting the best sensor readings to acquire, balancing the increase in the confidence of our answer against the communication and data acquisition costs in the network. We describe an exponential time algorithm for finding the optimal solution to this optimization problem, and a polynomialtime heuristic for identifying solutions that perform well in practice. We evaluate our approach on several realworld sensornetwork data sets, taking into account the real measured data and communication quality, demonstrating that our modelbased approach provides a highfidelity representation of the real phenomena and leads to significant performance gains versus traditional data acquisition techniques.
Distributed metric calibration of ad hoc camera networks
 ACM Trans. Sen. Netw
, 2006
"... We discuss how to automatically obtain the metric calibration of an adhoc network of cameras with no centralized processor. We model the set of uncalibrated cameras as nodes in a communication network, and propose a distributed algorithm in which each camera performs a local, robust bundle adjustme ..."
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Cited by 39 (4 self)
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We discuss how to automatically obtain the metric calibration of an adhoc network of cameras with no centralized processor. We model the set of uncalibrated cameras as nodes in a communication network, and propose a distributed algorithm in which each camera performs a local, robust bundle adjustment over the camera parameters and scene points of its neighbors in an overlay “vision graph”. We analyze the performance of the algorithm on both simulated and real data, and show that the distributed algorithm results in a fairer allocation of messages per node while achieving comparable calibration accuracy to centralized bundle adjustment.
Newscast EM
 In NIPS 17
, 2005
"... We propose a gossipbased distributed algorithm for Gaussian mixture learning, Newscast EM. The algorithm operates on network topologies where each node observes a local quantity and can communicate with other nodes in an arbitrary pointtopoint fashion. The main difference between Newscast EM and ..."
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Cited by 21 (1 self)
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We propose a gossipbased distributed algorithm for Gaussian mixture learning, Newscast EM. The algorithm operates on network topologies where each node observes a local quantity and can communicate with other nodes in an arbitrary pointtopoint fashion. The main difference between Newscast EM and the standard EM algorithm is that the Mstep in our case is implemented in a decentralized manner: (random) pairs of nodes repeatedly exchange their local parameter estimates and combine them by (weighted) averaging. We provide theoretical evidence and demonstrate experimentally that, under this protocol, nodes converge exponentially fast to the correct estimates in each Mstep of the EM algorithm. 1
A multifrontal QR factorization approach to distributed inference applied to multirobot localization and mapping
 AAAI National Conference on Artificial Intelligence
, 2005
"... QR factorization is most often used as a black box algorithm, but is in fact an elegant computation on a factor graph. By computing a rooted clique tree on this graph, the computation can be parallelized across subtrees, which forms the basis of socalled multifrontal QR methods. By judiciously c ..."
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Cited by 20 (7 self)
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QR factorization is most often used as a black box algorithm, but is in fact an elegant computation on a factor graph. By computing a rooted clique tree on this graph, the computation can be parallelized across subtrees, which forms the basis of socalled multifrontal QR methods. By judiciously choosing the order in which variables are eliminated in the clique tree computation, we show that one straightforwardly obtains a method for performing inference in distributed sensor networks. One obvious application is distributed localization and mapping with a team of robots. We phrase the problem as inference on a largescale Gaussian Markov Random Field induced by the measurement factor graph, and show how multifrontal QR on this graph solves for the global map and all the robot poses in a distributed fashion. The method is illustrated using both small and largescale simulations, and validated in practice through actual robot experiments.
Decentralized Data Fusion and Active Sensing with Mobile Sensors for Modeling and Predicting Spatiotemporal Traffic Phenomena
"... The problem of modeling and predicting spatiotemporal traffic phenomena over an urban road network is important to many traffic applications such as detecting and forecasting congestion hotspots. This paper presents a decentralized data fusion and active sensing (D 2 FAS) algorithm for mobile sensor ..."
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Cited by 19 (13 self)
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The problem of modeling and predicting spatiotemporal traffic phenomena over an urban road network is important to many traffic applications such as detecting and forecasting congestion hotspots. This paper presents a decentralized data fusion and active sensing (D 2 FAS) algorithm for mobile sensors to actively explore the road network to gather and assimilate the most informative data for predicting the traffic phenomenon. We analyze the time and communication complexity of D 2 FAS and demonstrate that it can scale well with a large number of observations and sensors. We provide a theoretical guarantee on its predictive performance to be equivalent to that of a sophisticated centralized sparse approximation for the Gaussian process (GP) model: The computation of such a sparse approximate GP model can thus be parallelized and distributed among the mobile sensors (in a Googlelike MapReduce paradigm), thereby achieving efficient and scalable prediction. We also theoretically guarantee its active sensing performance that improves under various practical environmental conditions. Empirical evaluation on realworld urban road network data shows that our D2FAS algorithm is significantly more timeefficient and scalable than stateoftheart centralized algorithms while achieving comparable predictive performance. 1
Calibrating Distributed Camera Networks Using Belief Propagation
"... We discuss how to obtain the accurate and globally consistent selfcalibration of a distributed camera network, in which camera nodes with no centralized processor may be spread over a wide geographical area. We present a distributed calibration algorithm based on belief propagation, in which each c ..."
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Cited by 17 (2 self)
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We discuss how to obtain the accurate and globally consistent selfcalibration of a distributed camera network, in which camera nodes with no centralized processor may be spread over a wide geographical area. We present a distributed calibration algorithm based on belief propagation, in which each camera node communicates only with its neighbors that image a sufficient number of scene points. The natural geometry of the system and the formulation of the estimation problem give rise to statistical dependencies that can be efficiently leveraged in a probabilistic framework. The camera calibration problem poses several challenges to information fusion, including overdetermined parameterizations and nonaligned coordinate systems. We suggest practical approaches to overcome these difficulties, and demonstrate the accurate and consistent performance of the algorithm using a simulated 30node camera network with varying levels of noise in the correspondences used for calibration, as well as an experiment with 15 real images. I.
Calibrating Distributed Camera Networks
, 2008
"... Recent developments in wireless sensor networks have made feasible distributed camera networks, in which cameras and processing nodes may be spread over a wide geographical area, with no centralized processor and limited ability to communicate a large amount of information over long distances. This ..."
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Cited by 14 (1 self)
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Recent developments in wireless sensor networks have made feasible distributed camera networks, in which cameras and processing nodes may be spread over a wide geographical area, with no centralized processor and limited ability to communicate a large amount of information over long distances. This paper overviews distributed algorithms for the calibration of such camera networks that is, the automatic estimation of each camera’s position, orientation, and focal length. In particular, we discuss a decentralized method for obtaining the vision graph for a distributed camera network, in which each edge of the graph represents two cameras that image a sufficiently large part of the same environment. We next describe a distributed algorithm in which each camera performs a local, robust nonlinear optimization over the camera parameters and scene points of its vision graph neighbors to obtain an initial calibration estimate. We then show how a distributed inference algorithm based on belief propagation can refine the initial estimate to be both accurate and globally consistent.
Using samplebased representations under communications constraints
 MIT, Laboratory for Information and Decision Systems
, 2004
"... In many applications, particularly powerconstrained sensor networks, it is important to conserve the amount of data exchanged while maximizing the utility of that data for some inference task. Broadly, this tradeoff has two major cost components—the representation’s size (in distributed networks, t ..."
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Cited by 13 (1 self)
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In many applications, particularly powerconstrained sensor networks, it is important to conserve the amount of data exchanged while maximizing the utility of that data for some inference task. Broadly, this tradeoff has two major cost components—the representation’s size (in distributed networks, the communications cost) and the error incurred by its use (the inference cost). We analyze this tradeoff for a particular problem: communicating a particlebased representation (and more generally, a Gaussian mixture or kernel density estimate). We begin by characterizing the exact communication cost of these representations, noting that it is less than might be suggested by traditional communications theory due to the invariance of the representation to reordering. We describe the optimal, lossless encoder when the generating distribution is known, and pose a suboptimal encoder which still benefits from reordering invariance. However, lossless encoding may not be sufficient. We describe one reasonable measure of error for distributionbased messages and its consequences for inference in an acyclic network, and propose a novel density approximation method based on KDtree multiscale representations which enables the communications cost and a bound on error to be balanced efficiently. We show several empirical examples demonstrating the method’s utility in collaborative, distributed signal processing under bandwidth or power constraints. 1