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20
Sensing Reality and Communicating Bits: A Dangerous Liaison
, 2006
"... [Is digital communication sufficient for sensor networks?] The successful design of sensor network architectures depends crucially on the structure of the sampling, observation, and communication processes. One of the most fundamental questions concerns the sufficiency of discrete approximations in ..."
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Cited by 20 (1 self)
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[Is digital communication sufficient for sensor networks?] The successful design of sensor network architectures depends crucially on the structure of the sampling, observation, and communication processes. One of the most fundamental questions concerns the sufficiency of discrete approximations in time, space, and amplitude. More explicitly, to capture the spatiotemporal variations of the underlying signals, when is it sufficient to build sensor network systems that work with discretetime andspace representations? And can the underlying amplitude variations of interest be observed at the highest possible fidelity if the sensors quantize their observations, assuming that quantization is done in the most sophisticated fashion, exploiting the principles of (ideal) distributed source coding? The former can be rephrased as the question of whether there is a spatiotemporal sampling theorem for typical data sets in sensor networks. This question has a positive answer in many cases of interest, based on the physics of the processes to be observed. The latter can be expressed as the question of whether there is a
Minimum Cost Data Aggregation with Localized Processing for Statistical Inference
 IN PROC. OF IEEE INFOCOM
, 2008
"... The problem of minimum cost innetwork fusion of measurements, collected from distributed sensors via multihop routing is considered. A designated fusion center performs an optimal statisticalinference test on the correlated measurements, drawn from a Markov random field. Conditioned on the deliver ..."
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Cited by 14 (9 self)
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The problem of minimum cost innetwork fusion of measurements, collected from distributed sensors via multihop routing is considered. A designated fusion center performs an optimal statisticalinference test on the correlated measurements, drawn from a Markov random field. Conditioned on the delivery of a sufficient statistic for inference to the fusion center, the structure of optimal routing and fusion is shown to be 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. The proposed fusion scheme involves routing packets of two types viz., raw measurements sent for local processing, and aggregates obtained on combining these processed values. The performance of heuristics for minimum cost fusion are evaluated through theory and simulations, showing a significant saving in routing costs, when compared to routing all the raw measurements to the fusion center.
Covariance estimation in decomposable Gaussian graphical models
 IEEE TRANSACTIONS ON SIGNAL PROCESSING
, 2010
"... Graphical models are a framework for representing and exploiting prior conditional independence structures within distributions using graphs. In the Gaussian case, these models are directly related to the sparsity of the inverse covariance (concentration) matrix and allow for improved covariance es ..."
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Cited by 12 (7 self)
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Graphical models are a framework for representing and exploiting prior conditional independence structures within distributions using graphs. In the Gaussian case, these models are directly related to the sparsity of the inverse covariance (concentration) matrix and allow for improved covariance estimation with lower computational complexity. We consider concentration estimation with the meansquared error (MSE) as the objective, in a special type of model known as decomposable. This model includes, for example, the well known banded structure and other cases encountered in practice. Our first contribution is the derivation and analysis of the minimum variance unbiased estimator (MVUE) in decomposable graphical models. We provide a simple closed form solution to the MVUE and compare it with the classical maximum likelihood estimator (MLE) in terms of performance and complexity. Next, we extend the celebrated Stein’s unbiased risk estimate (SURE) to graphical models. Using SURE, we prove that the MSE of the MVUE is always smaller or equal to that of the biased MLE, and that the MVUE itself is dominated by other approaches. In addition, we propose the use of SURE as a constructive mechanism for deriving new covariance estimators. Similarly to the classical MLE, all of our proposed estimators have simple closed form solutions but result in a significant reduction in MSE.
Decomposable Principal Component Analysis
"... Abstract—In this paper, we consider principal component analysis (PCA) in decomposable Gaussian graphical models. We exploit the prior information in these models in order to distribute PCA computation. For this purpose, we reformulate the PCA problem in the sparse inverse covariance (concentration) ..."
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Cited by 10 (6 self)
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Abstract—In this paper, we consider principal component analysis (PCA) in decomposable Gaussian graphical models. We exploit the prior information in these models in order to distribute PCA computation. For this purpose, we reformulate the PCA problem in the sparse inverse covariance (concentration) domain and address the global eigenvalue problem by solving a sequence of local eigenvalue problems in each of the cliques of the decomposable graph. We illustrate our methodology in the context of decentralized anomaly detection in the Abilene backbone network. Based on the topology of the network, we propose an approximate statistical graphical model and distribute the computation of PCA. Index Terms—Anomaly detection, graphical models, principal
Distributed Covariance Estimation in Gaussian Graphical Models
"... Abstract—We consider distributed estimation of the inverse covariance matrix in Gaussian graphical models. These models factorize the multivariate distribution and allow for efficient distributed signal processing methods such as belief propagation (BP). The classical maximum likelihood approach to ..."
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Cited by 7 (3 self)
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Abstract—We consider distributed estimation of the inverse covariance matrix in Gaussian graphical models. These models factorize the multivariate distribution and allow for efficient distributed signal processing methods such as belief propagation (BP). The classical maximum likelihood approach to this covariance estimation problem, or potential function estimation in BP terminology, requires centralized computing and is computationally intensive. This motivates suboptimal distributed alternatives that tradeoff accuracy for communication cost. A natural solution is for each node to perform estimation of its local covariance with respect to its neighbors. The local maximum likelihood estimator is asymptotically consistent but suboptimal, i.e., it does not minimize mean squared estimation (MSE) error. We propose to improve the MSE performance by introducing additional symmetry constraints using averaging and pseudolikelihood estimation approaches. We compute the proposed estimates using message passing protocols, which can be efficiently implemented in large scale graphical models with many nodes. We illustrate the advantages of our proposed methods using numerical experiments with synthetic data as well as real world data from a wireless sensor network. Index Terms—Covariance estimation, distributed signal processing, graphical models. I.
Spatial whitening framework for distributed estimation
 in Computational Advances in MultiSensor Adaptive Processing (CAMSAP), 2011 4th IEEE International Workshop on
, 2011
"... Abstract—Designing resource allocation strategies for power constrained sensor network in the presence of correlated data often gives rise to intractable problem formulations. In such situations, applying wellknown strategies derived from conditionalindependence assumption may turn out to be fair ..."
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Cited by 2 (2 self)
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Abstract—Designing resource allocation strategies for power constrained sensor network in the presence of correlated data often gives rise to intractable problem formulations. In such situations, applying wellknown strategies derived from conditionalindependence assumption may turn out to be fairly suboptimal. In this paper, we address this issue by proposing an adjacencybased spatial whitening scheme, where each sensor exchanges its observation with their neighbors prior to encoding their own private information and transmitting it to the fusion center. We comment on the computational limitations for obtaining the optimal whitening transformation, and propose an iterative optimization scheme to achieve the same for large networks. We demonstrate the efficacy of the whitening framework by considering the example of bitallocation for distributed estimation. I.
Principal component analysis in decomposable Gaussian graphical models
 in Proc. IEEE Int. Conf. Acoust., Speech Signal Process. (ICASSP 2009
, 2009
"... We consider principal component analysis (PCA) in decomposable Gaussian graphical models. We exploit the prior information in these models in order to distribute its computation. For this purpose, we reformulate the problem in the sparse inverse covariance (concentration) domain and solve the globa ..."
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Cited by 1 (0 self)
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We consider principal component analysis (PCA) in decomposable Gaussian graphical models. We exploit the prior information in these models in order to distribute its computation. For this purpose, we reformulate the problem in the sparse inverse covariance (concentration) domain and solve the global eigenvalue problem using a sequence of local eigenvalue problems in each of the cliques of the decomposable graph. We demonstrate the application of our methodology in the context of decentralized anomaly detection in the Abilene backbone network. Based on the topology of the network, we propose an approximate statistical graphical model and distribute the computation of PCA. Index Terms — Principal component analysis, graphical models, distributed data mining. 1.
Belief Propagation in Wireless Sensor Networks A Practical Approach
"... Abstract. Distributed inference schemes for detection, estimation and learning comprise an attractive approach to Wireless Sensor Networks (WSNs), because of properties such as asynchronous operation and robustness in the face of failures. Belief Propagation (BP) is a method for distributed inferenc ..."
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Abstract. Distributed inference schemes for detection, estimation and learning comprise an attractive approach to Wireless Sensor Networks (WSNs), because of properties such as asynchronous operation and robustness in the face of failures. Belief Propagation (BP) is a method for distributed inference which provides accurate results with rapid convergence properties. However, applying a BP algorithm to WSN is not trivial, due to the unique characteristics of WSN networks. Many papers which have proposed using BP for WSNs do not consider all of the constraints which these networks impose. This paper first undertakes a thorough study of the practical challenges of WSNs which are raised in the context of distributed inference. It then presents a framework which implements both localized and datacentric approaches to improve the effectiveness and the robustness of this algorithm in the WSN environment. The proposed solution is empirically evaluated, as applied to the clustering problem, and it can be easily extended to suit many other applications that use BP as an underlying algorithm.
Approval of the thesis: DECENTRALIZED ESTIMATION UNDER COMMUNICATION CONSTRAINTS
, 2009
"... Date: I hereby declare that all information in this document has been obtained and presented in accordance with academic rules and ethical conduct. I also declare that, as required by these rules and conduct, I have fully cited and referenced all material and results that are not original to this wo ..."
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Date: I hereby declare that all information in this document has been obtained and presented in accordance with academic rules and ethical conduct. I also declare that, as required by these rules and conduct, I have fully cited and referenced all material and results that are not original to this work.