Belief networks are directed acyclic graphs in which the nodes represent propositions (or variables), the arcs signify direct dependencies between the linked propositions, and the strengths of these dependencies are quantified by conditional probabilities. A network of this sort can be used to represent the generic knowledge of a domain expert, and it turns into a computational architecture if the links are used not merely for storing factual knowledge but also for directing and activating the data flow in the computations which manipulate this knowledge. The first part of the paper deals with the task of fusing and propagating the impacts of new information through the networks in such a way that, when equilibrium is reached, each proposition will be assigned a measure of belief consistent with the axioms of probability theory. It is shown that if the network is singly connected (e.g. tree-structured), then probabilities can be updated by local propagation in an isomorphic network of parallel and autonomous processors and that the impact of new information can be imparted to all propositions in time proportional to the longest path in the network. The second part of the paper deals with the problem of finding a tree-structured representation for a collection of probabilistically coupled propositions using auxiliary (dummy) variables, colloquially called "hidden causes. " It is shown that if such a tree-structured representation exists, then it is possible to uniquely uncover the topology of the tree by observing pairwise dependencies among the available propositions (i.e., the leaves of the tree). The entire tree structure, including the strengths of all internal relationships, can be reconstructed in time proportional to n log n, where n is the number of leaves.

. Probabilistic inference algorithms for belief updating, finding the most probable explanation, the maximum a posteriori hypothesis, and the maximum expected utility are reformulated within the bucket elimination framework. This emphasizes the principles common to many of the algorithms appearing in the probabilistic inference literature and clarifies the relationship of such algorithms to nonserial dynamic programming algorithms. A general method for combining conditioning and bucket elimination is also presented. For all the algorithms, bounds on complexity are given as a function of the problem's structure. 1. Overview Bucket elimination is a unifying algorithmic framework that generalizes dynamic programming to accommodate algorithms for many complex problemsolving and reasoning activities, including directional resolution for propositional satisfiability (Davis and Putnam, 1960), adaptive consistency for constraint satisfaction (Dechter and Pearl, 1987), Fourier and Gaussian el...

Graphical representations for probabilistic relationships have recently received considerable attention in A1. Qualitative probabilistic networks abstract from the usual numeric representations by encoding only qualitative relationships, which are inequality constraints on the joint probability distribution over the variables. Although these constraints are insufficient to determine probabilities uniquely, they are designed to justify the deduction of a class of relative likelihood conclusions that imply useful decision-making properties. Two types of qualitative relationship are defined, each a probabilistic form of monotonicity constraint over a group of variables. Qualitative influences describe the direction of the relationship between two variables. Qualitative synergies describe interactions among influences. The probabilistic definitions chosen justify sound and efficient inference procedures based on graphical manipulations of the network. These procedures answer queries about qualitative relationships among variables separated in the network and determine structural properties of optimal assignments to decision variables.

Pathfinder is an expert system that assists surgical pathologists with the diagnosis of lymph-node diseases. The program is one of a growing number of normative expert systems that use probability and decision theory to acquire, represent, manipulate, and explain uncertain medical knowledge. In this article, we describe Pathfinder and our research in uncertain-reasoning paradigms that was stimulated by the development of the program. We discuss limitations with early decision-theoretic methods for reasoning under uncertainty and our initial attempts to use non-decision-theoretic methods. Then, we describe experimental and theoretical results that directed us to return to reasoning methods based in probability and decision theory.

Given a knowledge base KB containing first-order and statistical facts, we consider a principled method, called the random-worlds method, for computing a degree of belief that some formula ' holds given KB . If we are reasoning about a world or system consisting of N individuals, then we can consider all possible worlds, or first-order models, with domain f1; : : : ; Ng that satisfy KB , and compute the fraction of them in which ' is true. We define the degree of belief to be the asymptotic value of this fraction as N grows large. We show that when the vocabulary underlying ' and KB uses constants and unary predicates only, we can naturally associate an entropy with each world. As N grows larger, there are many more worlds with higher entropy. Therefore, we can use a maximum-entropy computation to compute the degree of belief. This result is in a similar spirit to previous work in physics and artificial intelligence, but is far more general. Of equal interest to the result itself are...

Abstract—The substantial overhead of performing internal network monitoring motivates techniques for inferring spatially localized information about performance using only end-to-end measurements. In this paper, we present a novel methodology for inferring the queuing delay distributions across internal links in the network based solely on unicast, end-to-end measurements. The major contributions are: 1) we formulate a measurement procedure for estimation and localization of delay distribution based on end-to-end packet pairs; 2) we develop a simple way to compute maximum likelihood estimates (MLEs) using the expectation-maximization (EM) algorithm; 3) we develop a new estimation methodology based on recently proposed nonparametric, wavelet-based density estimation method; and 4) we optimize the computational complexity of the EM algorithm by developing a new fast Fourier transform implementation. Realistic network simulations are carried out using network-level simulator ns-2 to demonstrate the accuracy of the estimation procedure. Index Terms—Computer network performance, delay estimation, Internet, tomography. I.

The DUCK-calculus presented here is a recent approach to cope with probabilistic uncertainty in a sound and efficient way. Uncertain rules with bounds for probabilities and explicit conditional independences can be maintained incrementally. The basic inference mechanism relies on local bounds propagation, implementable by deductive databases with a bottom-up fixpoint evaluation. In situations, where no precise bounds are deducible, it can be combined with simple operations research techniques on a local scope. In particular, we provide new precise analytical bounds for probabilistic entailment.

Often experts are incapable of providing `exact' probabilities; likewise, samples on which the probabilities in networks are based must often be small and preliminary. In such cases the probabilities in the networks are imprecise. The imprecision can be handled by second-order probability distributions. It is convenient to use beta or Dirichlet distributions to express the uncertainty about probabilities. The problem of how to propagate point probabilities in a Bayesian network now is transformed into the problem of how to propagate Dirichlet distributions in Bayesian networks. It is shown that the propagation of Dirichlet distributions in Bayesian networks with incomplete data results in a system of probability mixtures of beta-binomial and Dirichlet distributions. Approximate first order probabilities and their second order probability density functions are be obtained by stochastic simulation. A number of properties of the propagation of imprecise probabilities are discuss...

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A computational system for reasoning about dynamic time-sliced systems using Bayesian networks is presented. The system, called dHugin, may be viewed as a generalization of the inference methods of classical discrete time-series analysis in the sense that it allows description of non-linear, discrete multivariate dynamic systems with complex conditional independence structures. The paper introduces the notions of dynamic time-sliced Bayesian networks, a dynamic time window, and common operations on the time window. Inference, pertaining to the time window and time slices preceding it, are formulated in terms of the well-known message passing scheme in junction trees [Jensen et al. (1990)]. Backward smoothing, for example, are performed efficiently through inter-tree message passing. Further, the system provides an ecient Monte-Carlo algorithm for forecasting; i.e., inference pertaining to time slices succeeding the time window. The system has been implemented on top of the Hugin shell [Andersen et al. (1989)].