The general problem of computing posterior probabilities in Bayesian networks is NP-hard (Cooper 1990). However efficient algorithms are often possible for particular applications by exploiting problem structures. It is well understood that the key to the materialization of such a possibility is to make use of conditional independence and work with factorizations of joint probabilities rather than joint probabilities themselves. Different exact approaches can be characterized in terms of their choices of factorizations. We propose a new approach which adopts a straightforward way for factorizing joint probabilities. In comparison with the clique tree propagation approach, our approach is very simple. It allows the pruning of irrelevant variables, it accommodates changes to the knowledge base more easily. it is easier to implement. More importantly, it can be adapted to utilize both intercausal independence and conditional independence in one uniform framework. On the other hand, clique tree propagation is better in terms of facilitating precomputations.

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.

This paper investigates the use of a class of importance sampling algorithms for probabilistic graphs in graphical structures. A general model for constructing importance sampling algorithms is given and then some particular cases are This work has been supported by the Commission of the European Communities under Project DRUMS 2 (Esprit BRA 6156) Address correspondence to Seraf'in Moral, Departamento de Ciencias de la Computaci 'on e IA, ETSI Inform'atica, Universidad de Granada, 18071 - Granada - Spain, e-mail:smc@robinson.ugr.es International Journal of Approximate Reasoning 1994 11:1--158 c fl 1994 Elsevier Science Inc. 655 Avenue of the Americas, New York, NY 10010 0888-613X/94/$7.00 2 considered. Logical sampling and likelihood weighting are particular cases of the model. Our proposal will be an algorithm which uses the functions with less entropy (more informative) to simulate the variables and the functions with more entropy to weight the simulations, in this way we expec...

We illustrate two different methodologies for learning Hybrid Bayesian networks, that is, Bayesian networks containing both continuous and discrete variables, from data. The two methodologies differ in the way of handling continuous data when learning the Bayesian network structure. The first methodology uses discretized data to learn the Bayesian network structure, and the original non-discretized data for the parameterization of the learned structure. The second methodology uses non-discretized data both to learn the Bayesian network structure and its parameterization. For the direct handling of continuous data, we propose the use of artificial neural networks as probability estimators, to be used as an integral part of the scoring metric defined to search the space of Bayesian network structures. With both methodologies, we assume the availability of a complete dataset, with no missing values or hidden variables. We report experimental results aimed at comparing the two methodologies. These results provide evidence that learning with discretized data presents advantages both in terms of efficiency and in terms of accuracy of the learned models over the alternative approach of using non-discretized data.

We extend continuous Gaussian networks − directed acyclic graphs that encode probabilistic relationships between variables − to its vector form. Vector Gaussian continuous networks consist of composite nodes representing multivariables, that take continuous values. These vector or composite nodes can represent correlations between parents, as opposed to conventional univariate nodes. We derive rules for inference in these networks based on two methods: message propagation and topology transformation. These two approaches lead to the development of algorithms, that can be implemented in either a centralized or a decentralized manner. The domain of application of these networks are monitoring and estimation problems. This new representation along with the rules for inference developed here can be used to derive current Bayesian algorithms such as the Kalman filter, and provide a rich foundation to develop new algorithms. We illustrate this process by deriving the decentralized form of the Kalman filter. This work unifies concepts from artificial intelligence and modern control theory. 1

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, ...

The general problem of computing posterior probabilities in Bayesian networks is NP-hard (Cooper 1990). However e cient algorithms are often possible for particular applications by exploiting problem structures. It is well understood that the key to the materialization of such a possibility istomake use of conditional independence and work with factorizations of joint probabilities rather than joint probabilities themselves. Di erent exact approaches can be characterized in terms of their choices of factorizations. We propose a new approach which adopts a straightforward way for factorizing joint probabilities. In comparison with the clique tree propagation approach, our approach isvery simple. It allows the pruning of irrelevantvariables, it accommodates changes to the knowledge base more easily. it is easier to implement. More importantly, it can be adapted to utilize both intercausal independence and conditional independence in one uniform framework. On the other hand, clique tree propagation is better in terms of facilitating precomputations.

This paper presents a new inference algorithm for belief networks that combines a search-based algorithm with a simulation-based algorithm. The former is an extension of the recursive decomposition (RD) al-gorithm proposed by Cooper in [8], which is here modi ed to compute interval bounds on marginal probabilities. We call the algorithm bounded-RD. The latter is a stochastic simulation method known as Pearl's Markov blanket algorithm [31]. Markov simulation is used to generate highly probable in-stantiations of the network nodes to be used by bounded-RD in the computation of probability bounds. Bounded-RD has the anytime property, and produces successively narrower interval bounds, which con-verge in the limit to the exact value. 1