20,400 research outputs found
Multi-view object tracking using sequential belief propagation
peer reviewedMultiple cameras and collaboration between them make possible the integration of information available from multiple views and reduce the uncertainty due to occlusions. This paper presents a novel method for integrating and tracking multi-view observations using bidirectional belief propagation. The method is based on a fully connected graphical model where target states at different views are represented as different but correlated random variables, and image observations at a given view are only associated with the target states at the same view. The tracking processes at different views collaborate with each other by exchanging information using a message passing scheme, which largely avoids propagating wrong information. An efficient sequential belief propagation algorithm is adopted to perform the collaboration and to infer the multi-view target states. We demonstrate the effectiveness of our method on video-surveillance sequences.TRICTRA
The Belief-Function Approach to Aggregating Audit Evidence
This is the peer reviewed version of the following article: Srivastava, R. P., "The Belief-Function Approach to Aggregating Audit Evidence" International Journal of Intelligent Systems, Vol. 10, No. 3, March 1995, pp. 329-356., which has been published in final form at http://doi.org/10.1002/int.4550100304. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.In this article, we present the belief-function approach to aggregating audit evidence. The approach uses an evidential network to represent the structure of audit evidence. In turn, it allows us to treat all types of dependencies and relationships among accounts and items of evidence, and thus the approach should help the auditor conduct an efficient and effective audit. Aggregation of evidence is equivalent to propagation of beliefs in an evidential network. The paper describes in detail the three major steps involved in the propagation process. The first step deals with drawing the evidential network representing the connections among variables and items of evidence, based on the experience and judgment of the auditor. We then use the evidential network to determine the clusters of variables over which we have belief functions. The second step deals with constructing a Markov tree from the clusters of variables determined in step one. The third step deals with the propagation of belief functions in the Markov tree. We use a moderately complex example to illustrate the details of the aggregation process
Convergence analysis of the information matrix in Gaussian belief propagation
Gaussian belief propagation (BP) has been widely used for distributed
estimation in large-scale networks such as the smart grid, communication
networks, and social networks, where local measurements/observations are
scattered over a wide geographical area. However, the convergence of Gaus- sian
BP is still an open issue. In this paper, we consider the convergence of
Gaussian BP, focusing in particular on the convergence of the information
matrix. We show analytically that the exchanged message information matrix
converges for arbitrary positive semidefinite initial value, and its dis- tance
to the unique positive definite limit matrix decreases exponentially fast.Comment: arXiv admin note: substantial text overlap with arXiv:1611.0201
Distributed Convergence Verification for Gaussian Belief Propagation
Gaussian belief propagation (BP) is a computationally efficient method to
approximate the marginal distribution and has been widely used for inference
with high dimensional data as well as distributed estimation in large-scale
networks. However, the convergence of Gaussian BP is still an open issue.
Though sufficient convergence conditions have been studied in the literature,
verifying these conditions requires gathering all the information over the
whole network, which defeats the main advantage of distributed computing by
using Gaussian BP. In this paper, we propose a novel sufficient convergence
condition for Gaussian BP that applies to both the pairwise linear Gaussian
model and to Gaussian Markov random fields. We show analytically that this
sufficient convergence condition can be easily verified in a distributed way
that satisfies the network topology constraint.Comment: accepted by Asilomar Conference on Signals, Systems, and Computers,
2017, Asilomar, Pacific Grove, CA. arXiv admin note: text overlap with
arXiv:1706.0407
Polynomial Linear Programming with Gaussian Belief Propagation
Interior-point methods are state-of-the-art algorithms for solving linear
programming (LP) problems with polynomial complexity. Specifically, the
Karmarkar algorithm typically solves LP problems in time O(n^{3.5}), where
is the number of unknown variables. Karmarkar's celebrated algorithm is known
to be an instance of the log-barrier method using the Newton iteration. The
main computational overhead of this method is in inverting the Hessian matrix
of the Newton iteration. In this contribution, we propose the application of
the Gaussian belief propagation (GaBP) algorithm as part of an efficient and
distributed LP solver that exploits the sparse and symmetric structure of the
Hessian matrix and avoids the need for direct matrix inversion. This approach
shifts the computation from realm of linear algebra to that of probabilistic
inference on graphical models, thus applying GaBP as an efficient inference
engine. Our construction is general and can be used for any interior-point
algorithm which uses the Newton method, including non-linear program solvers.Comment: 7 pages, 1 figure, appeared in the 46th Annual Allerton Conference on
Communication, Control and Computing, Allerton House, Illinois, Sept. 200
Distributed Local Linear Parameter Estimation using Gaussian SPAWN
We consider the problem of estimating local sensor parameters, where the
local parameters and sensor observations are related through linear stochastic
models. Sensors exchange messages and cooperate with each other to estimate
their own local parameters iteratively. We study the Gaussian Sum-Product
Algorithm over a Wireless Network (gSPAWN) procedure, which is based on belief
propagation, but uses fixed size broadcast messages at each sensor instead.
Compared with the popular diffusion strategies for performing network parameter
estimation, whose communication cost at each sensor increases with increasing
network density, the gSPAWN algorithm allows sensors to broadcast a message
whose size does not depend on the network size or density, making it more
suitable for applications in wireless sensor networks. We show that the gSPAWN
algorithm converges in mean and has mean-square stability under some technical
sufficient conditions, and we describe an application of the gSPAWN algorithm
to a network localization problem in non-line-of-sight environments. Numerical
results suggest that gSPAWN converges much faster in general than the diffusion
method, and has lower communication costs, with comparable root mean square
errors
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