: This article describes a propagation scheme for Bayesian networks with conditional Gaussian distributions that does not have the numerical weaknesses of the scheme derived in Lauritzen (1992). The propagation architecture is that of Lauritzen and Spiegelhalter (1988). In addition to the means and variances provided by the previous algorithm, the new propagation scheme yields full local marginal distributions. The new scheme also handles linear deterministic relationships between continuous variables in the network specification. The new propagation scheme is in many ways faster and simpler than previous schemes and the method has been implemented in the most recent version of the HUGIN software. Key words: Artificial intelligence, Bayesian networks, CG distributions, Gaussian mixtures, probabilistic expert systems, propagation of evidence. 1 Introduction Bayesian networks have developed into an important tool for building systems for decision support in environments characterized by...

This paper is about how to represent and solve decision problems in Bayesian decision theory (e.g. [6]). A general representation named decision networks is proposed based on influence diagrams [10]. This new representation incorporates the idea, from Markov decision process (e.g. [5]), that a decision may be conditionally independent of certain pieces of available information. It also allows multiple cooperative agents and facilitates the exploitation of separability in the utility function. Decision networks inherit the advantages of both influence diagrams and Markov decision processes, which makes them a better representation framework for decision analysis, planning under uncertainty, medical diagnosis and treatment.

This paper studies a variant of axioms originally developed by Shafer and Shenoy (1988). It is investigated which extra assumptions are needed to perform the local computations in a HUGIN-like architecture (Jensen et al. 1990) or in the architecture of Lauritzen and Spiegelhalter (1988). In particular it is shown that propagation of belief functions can be performed in these architectures. Keywords: articial intelligence, belief function, constraint propagation, expert system, probability propagation, valuation-based system. 1 Introduction An important development in articial intelligence is associated with an abstract theory of local computation known as the Shafer{Shenoy axioms (Shafer and Shenoy 1988; Shenoy and Shafer 1990). These describe in a very general setting how computations can be performed eciently and locally in a variety of problems, just if a few simple conditions are satised. Even though the axioms were developed to formalize computation with belief functions (Shaf...

In the last decade, several architectures have been proposed for exact computation of marginals using local computation. In this paper, we compare three architectures---Lauritzen-Spiegelhalter, Hugin, and Shenoy-Shafer---from the perspective of graphical structure for message propagation, message-passing scheme, computational efficiency, and storage efficiency. 1 INTRODUCTION In the last decade, several architectures have been proposed in the uncertain reasoning literature for exact computation of marginals of multivariate discrete probability distributions. One of the pioneering architectures for computing marginals was proposed by Pearl [1986]. Pearl's architecture applies to singly connected Bayes nets. For multiply connected Bayes nets, Pearl [1986] proposed the method of conditioning to reduce a multiply connected Bayes net to several singly connected Bayes nets. In 1988, Lauritzen and Spiegelhalter [1988] proposed an alternative architecture for computing marginals that applies...

The main aim of this paper is to describe two modifications to the Shenoy--Shafer architecture with the goal of making it computationally more efficient in computing marginals of the joint valuation. We also describe a modification to the Hugin architecture. Finally, we briefly compare the traditional and modified architectures by solving a couple of small Bayesian networks, and conclude with a statement of further research. 1998 Elsevier Science B.V. All rights reserved.

Stochastic independence is an idealized relationship located at one end of a continuum of values measuring degrees of dependence. Modeling real world systems, we are often not interested in the distinction between exact independence and any degree of dependence, but between weak ignorable and strong substantial dependence. Good models map significant deviance from independence and neglect approximate independence or dependence weaker than a noise threshold. This intuition is applied to learning the structure of Bayes nets from data. We determine the conditional posterior probabilities of structures given that the degree of dependence at each of their nodes exceeds a critical noise level. Deviance from independence is measured by mutual information. Arc probabilities are determined by the amount of mutual information the neighbors contribute to a node, is greater than a critical minimum deviance from independence. A Ø 2 approximation for the probability density function of mutual info...

As Bayesian networks become widely accepted as a normative formalism for diagnosis based on probabilistic knowledge, they are applied to increasingly larger problem domains. These large projects demand a systematic approach to handle the complexity in knowledge engineering. The needs include modularity in representation, distribution in computation, as well as coherence in inference. Multiply Sectioned Bayesian Networks (MSBNs) provide a distributed multiagent framework to address these needs. According to the framework, a large system is partitioned into subsystems and represented as a set of related Bayesian subnets. To ensure exact inference, the partition of a large system into subsystems and the representation of subsystems must follow a set of technical constraints. How to satisfy these goals for a given system may not be obvious to a practitioner. In this paper, we address three practical modeling issues.

Abstract—We consider a common task in multiagent systems where agents need to estimate the state of an uncertain domain so that they can act accordingly. If each agent only has partial knowledge about the domain and local observations, how can the agents accomplish the task with a limited amount of communication? Multiply sectioned Bayesian networks (MSBNs) provide an effective and exact framework for such a task but also impose a set of constraints. Are there simpler frameworks with the same performance but with less constraints? We identify a small set of high level choices which logically imply the key representational choices leading to MSBNs. The result addresses the necessity of constraints of the framework. It facilitates comparisons with related frameworks and provides guidance to potential extensions of the framework. (Keywords: multiagent system, decentralized interpretation, communication, organization structure, uncertain reasoning, probabilistic reasoning, belief network, Bayesian network) I.

A probabilistic framework is presented for assessing the uncertainties in simulation predictions that arise from model parameters derived from uncertain measurements. A probabilistic network facilitates both conceptualizing and computationally implementing an analysis of a large number of experiments in terms of many intrinsic models in a logically consistent manner. This approach permits one to improve one's knowledge about the underlying models at every level of the hierarchy of validation experiments. 1999 Elsevier Science B.V. All rights reserved.

Multiply sectioned Bayesian networks (MSBNs) provide a coherent and flexible formalism for representing uncertain knowledge in large domains. Global consistency among subnets in a MSBN is achieved by communication. When a subnet updates its belief with respect to an adjacent subnet, existing inference operations require repeated belief propagations (proportional to the number of linkages between the two subnets) within the receiving subnet, making communication less efficient. We redefine these operations such that two such propagations are sufficient. We prove that the new operations, while improving the efficiency, do not compromise the coherence. A MSBN must be initialized before inference can take place. The initialization involves dedicated operations not shared by inference operations according to existing methods. We show that the new inference operations presented here unify inference and initialization. Hence the new operations are not only more efficient but also s...