2008 To my wife, Martha. ii Acknowledgments This work would not have been possible without generous help, both intellectually and financially. I am grateful to my advisor, Satinder Singh, for the long discussions we have had as he has patiently taught me to think clearly through my own ideas, sharpen my writing, and to raise my sights. A special thanks also to my lab mates, Matt Rudary, Britton Wolfe, Vishal Soni, Erik Talviti, Jonathan Sorg and Ishan Chaudhuri for always letting me bounce ideas around, for listening, and for patient tutoring. Thanks to Andrew Nuxoll for being a kindred spirit, to Nick Gorski for the occasional foosball game and to my collaborators at the University of Alberta. Finally, I would like to gratefully acknowledge the National Science Foundation for financially supporting me through most of my studies with a Graduate Research Fellowship. Finally, a special thank you to my wife Martha for her love, her constancy, her feistiness and for always keeping me on the straight and narrow. Thank you, Grace, Peterson and Andrew for reminding

This report describes an investigation into the applicability of Bayesian networks for representing the uncertainty inherent in the characterization of containerized radiological waste. This research has been conducted by scientists at the Mississippi State University Diagnostic Instrumentation and Analysis Laboratory in collaboration with scientists at the Idaho National Engineering Laboratory. The goal is to develop an expert system that will assist in the determination of the proper disposition of radiological waste containers. Because the waste is typically assayed and examined nondestructively (i. e., without opening the containers), it is impossible to characterize the contents with certainty. The expert system will examine information including assay data and documentation for each waste container to determine if the waste meets the criteria for shipment to a permanent storage facility. Bayesian networks provide a mechanism for modeling the uncertainty in a domain using probabil...

Exponential Family PSR (EFPSR) models capture stochastic dynamical systems by representing state as the parameters of an exponential family distribution over a shortterm window of future observations. They are appealing from a learning perspective because they are fully observed (meaning expressions for maximum likelihood do not involve hidden quantities), but are still expressive enough to both capture existing models and predict new models. While maximumlikelihood learning algorithms for EFPSRs exist, they are not computationally feasible. We present a new, computationally efficient, learning algorithm based on an approximate likelihood function. The algorithm can be interpreted as attempting to induce stationary distributions of observations, features and states which match their empirically observed counterparts. The approximate likelihood, and the idea of matching stationary distributions, may apply to other models. 1.

Abstract—Markov random fields are designed to represent structured dependencies among large collections of random variables, and are well-suited to capture the structure of real-world signals. Many fundamental tasks in signal processing (e.g., smoothing, denoising, segmentation etc.) require efficient methods for computing (approximate) marginal probabilities over subsets of nodes in the graph. The marginalization problem, though solvable in linear time for graphs without cycles, is computationally intractable for general graphs with cycles. This intractability motivates the use of approximate “message-passing ” algorithms. This paper studies the convergence and stability properties of the family of reweighted sum-product algorithms, a generalization of the widely used sum-product or belief propagation algorithm, in which messages are adjusted with graph-dependent weights. For pairwise Markov random fields, we derive various conditions that are sufficient to ensure convergence, and also provide bounds on the geometric convergence rates. When specialized to the ordinary sum-product algorithm, these results provide strengthening of previous analyses. We prove that some of our conditions are necessary and sufficient for subclasses of homogeneous models, but not for general models. The experimental simulations on various classes of graphs validate our theoretical results. Index Terms—Approximate marginalization, belief propagation, convergence analysis, graphical models, Markov random fields, sum-product algorithm. I.

This dissertation is devoted to the design of an intelligent, distributed fault and performance management system for communication networks. The architecture is based on a distributed agent paradigm, with belief networks as the framework for knowledge representation and evidence propagation. The dissertation consists of four major parts. First, we choose the mobile code technology to help implement a distributed, extensible framework for supporting adaptive, dynamic network monitoring and control. The focus of our work is on three aspects. First, the design of the standard infrastructure, or Virtual Machine, based on which agents could be created, deployed, managed and initiated to run. Second, the collection API for our delegated agents to collect data from network elements. Third, the callback mechanism through whichthe functionality of the delegated agents or even the native software could be extended. We propose three system designs based on such ideas. Second, we propose a distributed framework for intelligent fault management purpose. The managed network is divided into several domains and for each

Abstract—Inference in general Markov random fields (MRFs) is NP-hard, though identifying the maximum a posteriori (MAP) configuration of pairwise MRFs with submodular cost functions is efficiently solvable using graph cuts. Marginal inference, however, even for this restricted class, is in #P. We prove new formulations of derivatives of the Bethe free energy, provide bounds on the derivatives and bracket the locations of stationary points, introducing a new technique called Bethe bound propagation. Several results apply to pairwise models whether associative or not. Applying these to discretized pseudo-marginals in the associative case we present a polynomial time approximation scheme for global optimization provided the maximum degree is O(log n), anddiscussseveralextensions. I.