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Presentation type: Other Presentations (Non-MURI-Affiliated) Date: 2004-05-19 Location: ICASSP, Montreal CAN Abstract/Description: Automatic self-calibration of ad-hoc sensor networks is a critical need for their use in military or civilian applications. In general, self-calibration involves the combination of absolute location information (e.g. GPS) with relative calibration information (e.g. estimated distance between sensors) over regions of the network. We formulate the self-calibration problem as a graphical model, enabling application of nonparametric belief propagation (NBP), a recent generalization of particle filtering, for both estimating sensor locations and representing location uncertainties. NBP has the advantage that it is easily implemented in a distributed fashion, can represent multi-modal uncertainty, and admits a wide variety of statistical models. This last point is particularly appealing in that it can be used to provide robustness against occasional high-variance (outlier) noise. We illustrate the performance of NBP using Monte Carlo analysis on an example network. URL
Presentation type: Other Presentations (Non-MURI-Affiliated) Date: 2004-04-27 Location: IPSN, Berkeley CA Abstract/Description: Automatic self-calibration of ad-hoc sensor networks is a critical need for their use in military or civilian applications. In general, self-calibration involves the combination of absolute location information (e.g. GPS) with relative calibration information (e.g. time delay or received signal strength between sensors) over regions of the network. Furthermore, it is generally desirable to distribute the computational burden across the network and minimize the amount of inter-sensor communication. We demonstrate that the information used for sensor calibration is fundamentally local with regard to the network topology and use this observation to reformulate the problem within a graphical model framework. We then demonstrate the utility of \\emph{nonparametric belief propagation} (NBP), a recent generalization of particle filtering, for both estimating sensor locations and representing location uncertainties. NBP has the advantage that it is easily implemented in a distributed fashion, admits a wide variety of statistical models, and can represent multi-modal uncertainty. We illustrate the performance of NBP on several example networks while comparing to a previously published nonlinear least squares method. URL
Presentation type: Other Presentations (Non-MURI-Affiliated) Date: 2004-02-20 Location: Brown University Vision and Learning Seminar Series Abstract/Description: Graphical models provide a powerful general framework for formulating and solving problems of statistical inference and machine learning. In many applications of graphical models, the hidden variables of interest are most naturally specified by continuous, non-Gaussian distributions. However, due to the limitations of existing inference algorithms, it is often necessary to form coarse, discrete approximations to such models. In this talk, we describe a nonparametric belief propagation (NBP) algorithm, that uses stochastic methods to propagate kernel-based approximations to the true continuous messages. Each NBP message update requires approximating the product of several Gaussian mixtures; we present efficient procedures for sampling from this product using multiscale representations. We demonstrate NBP\'s effectiveness on two different applications: visual recognition and tracking of complex objects, and distributed self-localization of an ad hoc sensor network. URL
Presentation type: Other Presentations (Non-MURI-Affiliated) Date: 2003-10-21 Location: MIT, Osbourne Room 35-338 Abstract/Description: A promising feature of emerging wireless sensor networks is the opportunity for each node to process data about \\\"locally\\\" sensed activity and then communicate relevant information output, altogether in a manner that supports \\\"globally\\\" effective decision-making. We consider a global objective of solving problems of detection, assuming each sensor node receives noisy measurements directly related to only its local environment. Within a usual Bayesian formulation, we present a simple two-node example for which our analysis exposes a fundamental tradeoff between costs due to decision errors and those due to communication overhead. Not surprisingly, this tradeoff is especially apparent when the activity local to one node is strongly correlated with activity local to the other node. It is easily argued that this tradeoff persists in networks with large numbers of sensor nodes, but we reveal that certain implicit assumptions underlying our otherwise appealing, two-node analysis can become impractical. We close with some ideas for future work, where the goal is to satisfy a more applicable set of assumptions for large sensor networks yet retain a quantifiable performance/communication tradeoff for distributed detection problems. URL
Presentation type: Official MURI Meetings (Other) Date: 2003-09-22 Location: Army Research Laboratory, Adelphi, MD Abstract/Description: - URL
Presentation type: Other Presentations (Non-MURI-Affiliated) Date: 2003-04-23 Location: IPSN 2003, Palo Alto, CA Abstract/Description: The issue of data association arises frequently in sensor networks; whenever multiple sensors and sources are present, it may be necessary to determine which observations from different sensors correspond to the same target. In highly uncertain environments, one may need to determine this correspondence without the benefit of an \\emph{a priori} known joint signal/sensor model. This paper examines the data association problem as the more general hypothesis test between factorizations of a single, learned distribution. The optimal test between known distributions may be decomposed into model-dependent and statistical dependence terms, quantifying the cost incurred by model estimation from measurements compared to a test between known models. We demonstrate how one might evaluate a two-signal association test efficiently using kernel density estimation methods to model a wide class of possible distributions, and show the resulting algorithm\'s ability to determine correspondence in uncertain conditions through a series of synthetic examples. We then describe an extension of this technique to multi-signal association which can be used to determine correspondence while avoiding the computationally prohibitive task of evaluating all hypotheses. Empirical results of the approximate approach are presented. URL
Presentation type: Official MURI Meetings (2nd Year Review) Date: 2002-06-14 Location: Army Research Laboratory, Adelphi, MD Abstract/Description: - URL
Presentation type: Official MURI Meetings (2nd Year Review) Date: 2002-06-14 Location: Army Research Laboratory, Adelphi, MD Abstract/Description: URL
Presentation type: Other Presentations (MURI Researchers) Date: 2002-04-22 Location: Yale University Abstract/Description: Many estimation tasks involve multiple heterogeneous or incomplete information sources. Modern classification problems, for example, have to be solved in the presence of predominantly unlabeled samples. Standard estimation algorithms in this context such as EM (or em) reduce to solving a set of fixed point equations (consistency conditions). Such algorithms are not stable, however, in the sense that they can lead to a dramatic loss of accuracy with the inclusion of incomplete observations (changes in the source allocation). We develop a more controlled solution to this problem through homotopy continuation, essentially evolving differential equations that govern the evolution of fixed points at intermediate allocations of the sources. We explicitly identify critical points along the resulting paths to either increase the stability of estimation or to ensure a significant departure from the initial source. We illustrate these ideas both in classification tasks with predominantly unlabeled data (text) as well as in the context of competitive min-max problems (DNA sequence motif discovery) URL
Presentation type: Other Presentations (MURI Researchers) Date: 2002-04-03 Location: Snowbird, Utah Abstract/Description: Bounds on the log partition function are important in a variety of contexts, including approximate inference, model fitting, decision theory, and large deviations analysis. We introduce a new class of upper bounds on the log partition function, based on convex combinations of distributions in the exponential domain, that is applicable to an arbitrary undirected graphical model. In the special case of convex combinations of tree-structured distributions, we obtain a family of variational problems, similar to the Bethe free energy, but distinguished by the following desirable properties: (i) {\\\\em they are convex, and have a unique global minimum;} and (ii) {\\\\em the global minimum gives an upper bound on the log partition function.} The global minimum is defined by stationary conditions very similar to those defining fixed points of belief propagation (BP) or tree-based reparameterization (Wainwright et al., 2001). As with BP fixed points, the elements of the minimizing argument can be used as approximations to the marginals of the original model. The analysis described here can be extended to more structured approximations (e.g., region graph and variants). URL
Presentation type: Other Presentations (MURI Researchers) Date: 2002-02-27 Location: Workshop on Information Theory, Mathematical Sciences Research Institute, Berkeley, CA Abstract/Description: Stochastic processes on graphs with cycles: Approximate inference and bounds Speaker: Martin Wainwright, MIT Joint work with Tommi Jaakkola and Alan Willsky, MIT Stochastic processes on graphs arise in a wide variety of fields, including coding theory, statistical physics, artificial intelligence, statistics, and network information theory. Graphical models provide a convenient language with which to formulate and study a variety of problems common to these fields. The first part of this talk will provide a brief tutorial introduction to the formalism of graphical models. We focus on Markov random fields defined on undirected graphs, including discussion of the Hammersley-Clifford theorem, as well as the junction tree representation. We then turn to the problem of inference in graphical models: i.e., estimating values of hidden random variables based on noisy observations. Although there exist very efficient algorithms for graphs without cycles (i.e., trees), the inference problem for a general graph with cycles is NP-complete, thereby motivating the use of approximate methods. The sum-product algorithm, also known as belief propagation (BP), is one of the best-known and most widely studied algorithms for computing approximate marginals. As an important example, it shows up as a highly successful iterative decoding method for various graphical codes (e.g., turbo codes, low-density parity check codes). In lieu of the usual message-passing analysis of BP, we develop the notion of reparameterization. This viewpoint leads to theoretical insight into the behavior of BP, including an intrinsic invariance, as well as a novel characterization of the fixed points. Moreover, we derive an exact expression (as well as computable bounds) for the approximation error (i.e., the difference betweeen BP approximate and exact marginals) on an arbitrary graph with cycles. Finally, we show how the notion of reparameterization and associated results apply to methods more advanced than BP (e.g., Kikuchi). Time permitting, we shall also discuss bounds on the log partition function. Such bounds have applications in various information-theoretic contexts, including approximate inference, large deviations analysis, and bounds on capacity and rate distortion. We present a new class of upper bounds that arise from convexified versions of the Bethe/Kikuchi free energy. Our development is based on convex analysis, and associated ideas from information geometry. URL
Presentation type: Official MURI Meetings (1st Year Review) Date: 2001-06-18 Location: Army Research Laboratory, Adelphi, MD Abstract/Description: URL
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