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15
Estimation in Gaussian Graphical Models Using Tractable Subgraphs: A WalkSum Analysis
, 2008
"... Graphical models provide a powerful formalism for statistical signal processing. Due to their sophisticated modeling capabilities, they have found applications in a variety of fields such as computer vision, image processing, and distributed sensor networks. In this paper, we present a general clas ..."
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Cited by 15 (11 self)
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Graphical models provide a powerful formalism for statistical signal processing. Due to their sophisticated modeling capabilities, they have found applications in a variety of fields such as computer vision, image processing, and distributed sensor networks. In this paper, we present a general class of algorithms for estimation in Gaussian graphical models with arbitrary structure. These algorithms involve a sequence of inference problems on tractable subgraphs over subsets of variables. This framework includes parallel iterations such as embedded trees, serial iterations such as block Gauss–Seidel, and hybrid versions of these iterations. We also discuss a method that uses local memory at each node to overcome temporary communication failures that may arise in distributed sensor network applications. We analyze these algorithms based on the recently developed walksum interpretation of Gaussian inference. We describe the walks “computed ” by the algorithms using walksum diagrams, and show that for iterations based on a very large and flexible set of sequences of subgraphs, convergence is guaranteed in walksummable models. Consequently, we are free to choose spanning trees and subsets of variables adaptively at each iteration. This leads to efficient methods for optimizing the next iteration step to achieve maximum reduction in error. Simulation results demonstrate that these nonstationary algorithms provide a significant speedup in convergence over traditional onetree and twotree iterations.
DISTRIBUTED KALMAN FILTERS IN SENSOR NETWORKS: BIPARTITE FUSION GRAPHS
, 2007
"... We study the distributed Kalman filter in sensor networks where multiple sensors collaborate to achieve a common objective. Our motivation is to distribute the global model that comes from the statespace representation of a sparse and localized largescale system into reduced coupled sensorbased mo ..."
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Cited by 6 (2 self)
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We study the distributed Kalman filter in sensor networks where multiple sensors collaborate to achieve a common objective. Our motivation is to distribute the global model that comes from the statespace representation of a sparse and localized largescale system into reduced coupled sensorbased models. We implement local Kalman filters on these reduced models, by approximating the Gaussian error process of the Kalman filter to be GaussMarkov, ensuring that each sensor is involved only in reducedorder computations and local communication. We propose a generalized distributed Jacobi algorithm to compute global matrix inversion, locally, in an iterative fashion. We employ bipartite fusion graphs in order to fuse the shared observations and shared estimates across the local models.
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 4 (1 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.
DISTRIBUTED ITERATECOLLAPSE INVERSION (DICI) ALGORITHM FOR LBANDED MATRICES
, 2008
"... In this paper, we present a distributed algorithm to invert L−banded matrices that are symmetric positive definite (SPD), when the submatrices in the band are distributed among several processing nodes. We provide a distributed iteratecollapse inversion (DICI) algorithm that converges, at each node ..."
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Cited by 3 (3 self)
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In this paper, we present a distributed algorithm to invert L−banded matrices that are symmetric positive definite (SPD), when the submatrices in the band are distributed among several processing nodes. We provide a distributed iteratecollapse inversion (DICI) algorithm that converges, at each node, to the corresponding submatrices in the inverse of the L−banded matrix. The computational complexity of the DICI algorithm to invert an SPD L−banded n × n matrix can be shown at each node to be independent of the size, n, of the matrix. Local information exchange is carried out after each iteration to guarantee convergence. We apply this algorithm to invert the information matrices in a computationally efficient distributed implementation of the Kalman filter and show its application towards inverting arbitrary sparse SPD matrices.
Modeling and estimation in Gaussian graphical models: Maximumentropy relaxation and walksum analysis
 Master’s thesis, Massachusetts Inst
, 2007
"... models provide a powerful formalism for statistical signal processing. Due to ..."
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Cited by 2 (1 self)
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models provide a powerful formalism for statistical signal processing. Due to
Gaussian Multiresolution Models: Exploiting Sparse Markov and Covariance Structure
 IEEE Trans. on Signal. Proc
, 2010
"... Abstract—In this paper, we consider the problem of learning Gaussian multiresolution (MR) models in which data are only available at the finest scale, and the coarser, hidden variables serve to capture longdistance dependencies. Treestructured MR models have limited modeling capabilities, as varia ..."
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Abstract—In this paper, we consider the problem of learning Gaussian multiresolution (MR) models in which data are only available at the finest scale, and the coarser, hidden variables serve to capture longdistance dependencies. Treestructured MR models have limited modeling capabilities, as variables at one scale are forced to be uncorrelated with each other conditioned on other scales. We propose a new class of Gaussian MR models in which variables at each scale have sparse conditional covariance structure conditioned on other scales. Our goal is to learn a treestructured graphical model connecting variables across scales (which translates into sparsity in inverse covariance), while at the same time learning sparse structure for the conditional covariance (not its inverse) within each scale conditioned on other scales. This model leads to an efficient, new inference algorithm that is similar to multipole methods in computational physics. We demonstrate the modeling and inference advantages of our approach over methods that use MR tree models and singlescale approximation methods that do not use hidden variables. Index Terms—Gauss–Markov random fields, graphical models, hidden variables, multipole methods, multiresolution (MR) models. I.
Timespacesequential algorithms for distributed Bayesian state estimation in serial sensor networks
 in Proc. IEEE ICASSP09
, 2009
"... We consider distributed estimation of a timedependent, random state vector based on a generally nonlinear/nonGaussian statespace model. The current state is sensed by a serial sensor network without a fusion center. We present an optimal distributed Bayesian estimation algorithm that is sequenti ..."
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Cited by 1 (0 self)
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We consider distributed estimation of a timedependent, random state vector based on a generally nonlinear/nonGaussian statespace model. The current state is sensed by a serial sensor network without a fusion center. We present an optimal distributed Bayesian estimation algorithm that is sequential both in time and in space (i.e., across sensors) and requires only local communication between neighboring sensors. For the linear/Gaussian case, the algorithm reduces to a timespacesequential, distributed form of the Kalman filter. We also demonstrate the application of our state estimator to a target tracking problem, using a dynamically defined “local sensor chain ” around the current target position. Index Terms—Parameter estimation, state estimation, sequential Bayesian filtering, distributed inference, sensor networks, Kalman filter, target tracking. 1.
Multiscale Gaussian Graphical Models and . . .
, 2007
"... Graphical models provide a powerful framework for stochastic processes by representing dependencies among random variables compactly with graphs. In particular, multiscale treestructured graphs have attracted much attention for their computational efficiency as well as their ability to capture long ..."
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Graphical models provide a powerful framework for stochastic processes by representing dependencies among random variables compactly with graphs. In particular, multiscale treestructured graphs have attracted much attention for their computational efficiency as well as their ability to capture longrange correlations. However, tree models have limited modeling power that may lead to blocky artifacts. Previous works on extending trees to pyramidal structures resorted to computationally expensive methods to get solutions due to the resulting model complexity. In this thesis, we propose a pyramidal graphical model with rich modeling power for Gaussian processes, and develop efficient inference algorithms to solve largescale estimation problems. The pyramidal graph has statistical links between pairs of neighboring nodes within each scale as well as between adjacent scales. Although the graph has many cycles, its hierarchical structure enables us to develop a class of fast
1 Estimation in Gaussian Graphical Models using Tractable Subgraphs: A WalkSum Analysis
"... Abstract — Graphical models provide a powerful formalism for statistical signal processing. Due to their sophisticated modeling capabilities, they have found applications in a variety of fields such as computer vision, image processing, and distributed sensor networks. In this paper, we present a ge ..."
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Abstract — Graphical models provide a powerful formalism for statistical signal processing. Due to their sophisticated modeling capabilities, they have found applications in a variety of fields such as computer vision, image processing, and distributed sensor networks. In this paper, we present a general class of algorithms for estimation in Gaussian graphical models with arbitrary structure. These algorithms involve a sequence of inference problems on tractable subgraphs over subsets of variables. This framework includes parallel iterations such as Embedded Trees, serial iterations such as block GaussSeidel, and hybrid versions of these iterations. We also discuss a method that uses local memory at each node to overcome temporary communication failures that may arise in distributed sensor network applications. We analyze these algorithms based on the recently developed walksum interpretation of Gaussian inference. We describe the walks “computed ” by the algorithms using walksum diagrams, and show that for iterations based on a very large and flexible set of sequences of subgraphs, convergence is guaranteed in walksummable models. Consequently, we are free to choose spanning trees and subsets of variables adaptively at each iteration. This leads to efficient methods for optimizing the next iteration step to achieve maximum reduction in error. Simulation results demonstrate that these nonstationary algorithms provide a significant speedup in convergence over traditional onetree and twotree iterations. Index Terms — Graphical models, GaussMarkov Random Fields, walksums, distributed estimation, walksum diagrams,
OPTIMISATION OF THE VLSI ARCHITECTURE IN WIRELESS SENSOR NETWORK
"... Optimisation of vlsi architecture in wireless sensor network (WSN) scheme for fusion centre to detect the faults of sensor nodes via efficient collaborative sensor fault detection (ECSFD), these scheme identifies the sensor node fault percentage and its efficiency of the particular sensor node. In r ..."
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Optimisation of vlsi architecture in wireless sensor network (WSN) scheme for fusion centre to detect the faults of sensor nodes via efficient collaborative sensor fault detection (ECSFD), these scheme identifies the sensor node fault percentage and its efficiency of the particular sensor node. In real world most of the applications of WSN are based on ASIC and the standalone devices. So this optimized efficient collaborative wireless sensor fault detection scheme is less expensive area of the chip is very less and fast in performance. Index Terms — Wireless sensor network, Collaborative sensor fault detection, Efficient collaborative sensor fault