Detection of Gauss-Markov Random Fields with Nearest-Neighbor Dependency

Anandkumar, Animashree; Tong, Lang; Swami, Ananthram

doi:10.21236/ada536158

Cited by 20 publications

(45 citation statements)

References 43 publications

(115 reference statements)

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“…We adopt the Markov model proposed in [8], where the correlation between neighboring nodes i and j is expressed as a function c(r ij ) of the inter-node distance r ij .…”

Section: Numerical Resultsmentioning

confidence: 99%

“…3 is defined applying the elementwise mapping z(a ij ) : R → R + given in (8). We can notice that, although the second term in (9)…”

Section: Encouraging Sparsity By Preserving Total Transmit Powermentioning

confidence: 99%

“…7 The detailed proof can be found in [15]. 8 We denote with |A| the matrix with entries |a ij | = a + ij + a − ij .…”

Section: Encouraging Sparsity By Preserving Total Transmit Powermentioning

confidence: 99%

“…Sparsity is encouraged introducing in our optimization procedure a penalty term that penalizes the presence of links in the WSN among power consuming distant nodes. A basic assumption underlying our approach is that the links among nodes of the dependency graph occur only between non distant nodes, as proposed for example in [8].…”

Section: Introductionmentioning

confidence: 99%

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Energy preserving matching of sensor network topology to dependency graph of the observed field

Sardellitti

Barbarossa

2011

2011 17th International Conference on Digital Signal Processing (DSP)

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The goal of this paper is to design the topology of a wireless sensor network observing a Markov random field in order to match the structure of the dependency graph of the observed field, under constraints on the energy spent to maintain the sensor network connectivity. The approach is important to enable the implementation of belief propagation algorithms at the network level, to achieve optimal decisions requiring simple message passing mechanisms among nearby nodes. Our main task is to recover the sparsity of the dependency graph and to replicate it at the sensor network level, under the constraint of limiting the transmit power necessary to establish the link among the nodes. To avoid the computational burden of the combinatorial problem associated to the topology design, we devise ad hoc relaxation techniques that allow us to achieve the solution through efficient algorithms based on difference of convex problems. © 2011 IEEE

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“…We adopt the Markov model proposed in [8], where the correlation between neighboring nodes i and j is expressed as a function c(r ij ) of the inter-node distance r ij .…”

Section: Numerical Resultsmentioning

confidence: 99%

“…3 is defined applying the elementwise mapping z(a ij ) : R → R + given in (8). We can notice that, although the second term in (9)…”

Section: Encouraging Sparsity By Preserving Total Transmit Powermentioning

confidence: 99%

“…7 The detailed proof can be found in [15]. 8 We denote with |A| the matrix with entries |a ij | = a + ij + a − ij .…”

Section: Encouraging Sparsity By Preserving Total Transmit Powermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Energy preserving matching of sensor network topology to dependency graph of the observed field

Sardellitti

Barbarossa

2011

2011 17th International Conference on Digital Signal Processing (DSP)

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“…The RHT problem is more general since the form of the classifier depends on the distribution of each hypothesis. References [10][11][12] study the use of graphical models in hypothesis testing, however, these works do not design robust tests.…”

Section: Introductionmentioning

confidence: 99%

Scalable robust hypothesis tests using graphical models

Vats

Monga

Srinivas

et al. 2011

2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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Traditional binary hypothesis testing relies on the precise knowledge of the probability density of an observed random vector conditioned on each hypothesis. However, for many applications, these densities can only be approximated due to limited training data or dynamic changes affecting the observed signal. A classical approach to handle such scenarios of imprecise knowledge is via minimax robust hypothesis testing (RHT), where a test is designed to minimize the worst case performance for all models in the vicinity of the approximated imprecise density. Despite the promise of RHT for robust classification problems, its applications have remained rather limited because RHT in its native form does not scale gracefully with the dimension of the observed random vector. In this paper, we use approximations via probabilistic graphical models, in particular block-tree graphs, to enable computationally tractable algorithms for realizing RHT on high-dimensional data. We quantify the reductions in computational complexity. Experimental results on simulated data and a target recognition problem show minimal loss over a true RHT.

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Cost-performance tradeoff in multi-hop aggregation for statistical inference

Anandkumar

Tong

Swami

et al. 2008

2008 IEEE International Symposium on Information Theory

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The problem of distributed fusion for binary hypothesis testing in a multihop network is considered. The sensor measurements are spatially correlated according to a Markov random field (MRF) under both the hypotheses. A fusion scheme for detection involves selection and localized processing of a subset of sensor measurements, fusion of these processed values to form a sufficient statistic, and its delivery to the fusion center. The goal is to find a fusion scheme that achieves optimal linear tradeoff between the total routing costs and the resulting detection error exponent at the fusion center. The Neyman-Pearson error exponent, under a fixed type-I bound, is shown to be the limit of the normalized sum of the Kullback-Leibler distances (KLD) over the maximal cliques of the MRF under some convergence conditions. It is shown that optimal fusion reduces to a prizecollecting Steiner tree (PCST) with the approximation factor preserved when the cliques of the MRF are disjoint. The PCST is found over an expanded communication graph with virtual nodes added for each non-trivial maximal clique of the MRF and their KLD assigned as the node penalty.

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Detection of Gauss-Markov Random Fields with Nearest-Neighbor Dependency

Cited by 20 publications

References 43 publications

Energy preserving matching of sensor network topology to dependency graph of the observed field

Energy preserving matching of sensor network topology to dependency graph of the observed field

Scalable robust hypothesis tests using graphical models

Cost-performance tradeoff in multi-hop aggregation for statistical inference

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