ion Modulation In many cases, it may be more useful to do normative inference on a model that is deemed to be complete at a particular level of abstraction than it is to do an approximate or heuristic analysis of a model that is too large to be analyzed under specific resource constraints. It may prove useful in many cases to store several belief-network representations, each containing propositions at different levels of abstraction. In many domains, models at higher levels of abstraction are more tractable. As the time available for computation decreases, network modules of increasing abstraction can be employed. ffl Local Reformulation Local reformulation is the modification of specific troublesome topologies in a belief network. Approximation methods and heuristics designed to modify the microstructure of belief networks will undoubtedly be useful in the tractable solution of large uncertain-reasoning problems. Such strategies might be best applied at knowledge-encoding time. An...

Despite their different perspectives, artificial intelligence (AI) and the disciplines of decision science have common roots and strive for similar goals. This paper surveys the potential for addressing problems in representation, inference, knowledge engineering, and explanation within the decision-theoretic framework. Recent analyses of the restrictions of several traditional AI reasoning techniques, coupled with the development of more tractable and expressive decisiontheoretic representation and inference strategies, have stimulated renewed interest in decision theory and decision analysis. We describe early experience with simple probabilistic schemes for automated reasoning, review the dominant expert-system paradigm, and survey some recent research at the crossroads of AI and decision science. In particular, we present the belief network and influence diagram representations. Finally, we discuss issues that have not been studied in detail within the expert-systems sett...

As Bayesian networks are applied to more complex and realistic real-world applications, the development of more efficient inference algorithms working under real-time constraints is becoming more and more important. This paper presents a survey of various exact and approximate Bayesian network inference algorithms. In particular, previous research on real-time inference is reviewed. It provides a framework for understanding these algorithms and the relationships between them. Some important issues in real-time Bayesian networks inference are also discussed.

In this abstract we give an overview of the work described in [15]. Belief networks provide a graphical representation of causal relationships together with a mechanism for probabilistic inference, allowing belief updating based on incomplete and dynamic information. We present a survey of Belief Network belief updating algorithms and propose a domain characterisation system which is used as a basis for algorithm comparison. We give experimental comparative results of algorithm performance using the proposed framework. We show how domain characterisation may be used to predict algorithm performance. Introduction Belief networks are directed acyclic graphs, where nodes correspond to random variables, which are usually assumed to take discrete values. The relationship between any set of state variables can be specified by a joint probability distribution. The nodes in the network are connected by directed arcs, which may be thought of as causal or influence links. The connections also ...

This paper describes an algorithmic means for inducing implication networks from empirical data samples. The induced network enables efficient inferences about the values of network nodes if certain observations are made. This implication induction method is approximate in nature as probablistic network requirements are relaxed in the construction of dependence relationships based on statistical testing. In order to examine the effectiveness and validity of the induction method, several Monte-Carlo simulations were conducted where theoretical Bayesian networks were used to generate empirical data samples \Gamma some of which were used to induce implication relations whereas others were used to verify the results of evidential reasoning with the induced networks. The values in the implication networks were predicted by applying a modified version of Dempster-Shafer belief updating scheme. The results of predictions were, furthermore, compared to the ones generated by Pearl's stochastic ...

In this paper a new algorithm for the propagation of probabilities in junction trees is presented. It is based on an hybrid methodology. Given a junction tree, some of the nodes carry out and exact calculation, and the other an approximation by Monte-Carlo methods. A general class of importance sampling algorithms is used for the Monte-Carlo estimation. The basic algorithm and some variations of it are presented. An experimental evaluation is carried out, comparing their performance with the well known likelihood weighting approximated algorithm.

Researchers in artificial intelligence and decision analysis share a concern with the construction of formal models of human knowledge and expertise. Historically, however, their approaches to these problems have diverged. Members of these two communities have recently discovered common ground: a family of graphical models of decision theory known as influence diagrams or as belief networks. These models are equally attractive to theoreticians, decision modelers, and designers of knowledge-based systems. From a theoretical perspective, they combine graph theory, probability theory and decision theory. From an implementation perspective, they lead to powerful automated systems. Although many practicing decision analysts have already adopted influence diagrams as modeling and structuring tools, they may remain unaware of the theoretical work that has emerged from the artificial intelligence community. This paper surveys the first decade or so of this work. Investment Technology Group, ...

In recent years belief networks have become a popular representation for reasoning under uncertainty and are used in a wide variety of applications. There are a number of exact and approximate inference algorithms available for performing belief updating, however in general the task is NP-hard. To overcome the problems of computational complexity that occur when modelling larger, real-world problems, researchers have developed variants of stochastic simulation approximation algorithms, and a number of other approaches involve approximating the model or limiting belief updating to nodes of interest. Typically comparisons are made of only a few algorithms, and on a particular example network. We survey the belief network algorithms and propose a system for domain characterisation as a basis for algorithm comparison. We present performance results using this framework from three sets of experiments: (1) on the Likelihood Weighting (LW) and Logic Sampling (LS) stochastic simulation algorithms; (2) on the performance of LW and Jensen's algorithms on state-space abstracted networks, (3) some comparisons of the time performance of LW, LS and the Jensen algorithm. Our results indicate that domain characterisation may be useful for predicting inference algorithm performance on a belief network for a new application domain.

We present a new framework for implementing evaluation of belief networks (BNs), which consists of two steps: (1) transforming a belief network into a tree structure called a treeNet (2) performing anytime inference by searching the treeNet. The root of the treeNet represents the query node. Once the treeNet has been constructed, whenever new evidence is incorporated, the posterior probability of the query node is re-calculated, using a variation of the polytree message-passing algorithm. The treeNet framework is geared towards anytime evaluation. Evaluating the treeNet is a tree search problem and we investigate different tree search strategies. By using a best-first method, we are able to increase the rate of convergence of the anytime result.

We present a method for mapping a given Bayesian network to a Boltzmann machine architecture, in the sense that the the updating process of the resulting Boltzmann machine model provably converges to a state which can be mapped back to a maximum a posteriori (MAP) probability state in the probability distribution represented by the Bayesian network. The Boltzmann machine model can be implemented efficiently on massively parallel hardware, since the resulting structure can be divided into two separate clusters where all the nodes in one cluster can be updated simultaneously. This means that the proposed mapping can be used for providing Bayesian network models with a massively parallel probabilistic reasoning module, capable of finding the MAP states in a computationally efficient manner. From the neural network point of view, the mapping from a Bayesian network to a Boltzmann machine can be seen as a method for automatically determining the structure and the connection weights of a Boltzmann machine by incorporating high-level, probabilistic information directly into the neural network architecture, without recourse to a time-consuming and unreliable learning process.