Distributed data association for multi-target tracking in sensor networks

Associating sensor measurements with target tracks is a fundamental and challenging problem in multi-target tracking. The problem is even more challenging in the context of sensor networks, since association is coupled across the network, yet centralized data processing is in general infeasible due to power and bandwidth limitations. Hence efficient, distributed solutions are needed. We propose techniques based on graphical models to efficiently solve such data association problems in sensor networks. Our approach scales well with the number of sensor nodes in the network, and it is well--suited for distributed implementation. Distributed inference is realized by a message--passing algorithm which requires iterative, parallel exchange of information among neighboring nodes on the graph. So as to address trade--offs between inference performance and communication costs, we also propose a communication--sensitive form of message--passing that is capable of achieving near--optimal performance using far less communication. We demonstrate the effectiveness of our approach with experiments on simulated data

Consensus Propagation

We propose consensus propagation, an asynchronous distributed protocol for averaging numbers across a network. We establish convergence, characterize the convergence rate for regular graphs, and demonstrate that the protocol exhibits better scaling properties than pairwise averaging, an alternative that has received much recent attention. Consensus propagation can be viewed as a special case of belief propagation, and our results contribute to the belief propagation literature. In particular, beyond singly-connected graphs, there are very few classes of relevant problems for which belief propagation is known to converge.Comment: journal versio

Sufficient conditions for convergence of the Sum-Product Algorithm

We derive novel conditions that guarantee convergence of the Sum-Product algorithm (also known as Loopy Belief Propagation or simply Belief Propagation) to a unique fixed point, irrespective of the initial messages. The computational complexity of the conditions is polynomial in the number of variables. In contrast with previously existing conditions, our results are directly applicable to arbitrary factor graphs (with discrete variables) and are shown to be valid also in the case of factors containing zeros, under some additional conditions. We compare our bounds with existing ones, numerically and, if possible, analytically. For binary variables with pairwise interactions, we derive sufficient conditions that take into account local evidence (i.e., single variable factors) and the type of pair interactions (attractive or repulsive). It is shown empirically that this bound outperforms existing bounds.Comment: 15 pages, 5 figures. Major changes and new results in this revised version. Submitted to IEEE Transactions on Information Theor

Approximate inference in Gaussian graphical models

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2008.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Includes bibliographical references (p. 161-169).The focus of this thesis is approximate inference in Gaussian graphical models. A graphical model is a family of probability distributions in which the structure of interactions among the random variables is captured by a graph. Graphical models have become a powerful tool to describe complex high-dimensional systems specified through local interactions. While such models are extremely rich and can represent a diverse range of phenomena, inference in general graphical models is a hard problem. In this thesis we study Gaussian graphical models, in which the joint distribution of all the random variables is Gaussian, and the graphical structure is exposed in the inverse of the covariance matrix. Such models are commonly used in a variety of fields, including remote sensing, computer vision, biology and sensor networks. Inference in Gaussian models reduces to matrix inversion, but for very large-scale models and for models requiring distributed inference, matrix inversion is not feasible. We first study a representation of inference in Gaussian graphical models in terms of computing sums of weights of walks in the graph -- where means, variances and correlations can be represented as such walk-sums. This representation holds in a wide class of Gaussian models that we call walk-summable. We develop a walk-sum interpretation for a popular distributed approximate inference algorithm called loopy belief propagation (LBP), and establish conditions for its convergence. We also extend the walk-sum framework to analyze more powerful versions of LBP that trade off convergence and accuracy for computational complexity, and establish conditions for their convergence. Next we consider an efficient approach to find approximate variances in large scale Gaussian graphical models.(cont.) Our approach relies on constructing a low-rank aliasing matrix with respect to the Markov graph of the model which can be used to compute an approximation to the inverse of the information matrix for the model. By designing this matrix such that only the weakly correlated terms are aliased, we are able to give provably accurate variance approximations. We describe a construction of such a low-rank aliasing matrix for models with short-range correlations, and a wavelet based construction for models with smooth long-range correlations. We also establish accuracy guarantees for the resulting variance approximations.by Dmitry M. Malioutov.Ph.D