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.

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.

Data dependencies are used in database schema design to enforce the correctness of a database as well as to reduce redundant data. These dependencies are usually determined from the semantics of the attributes and are then enforced upon the relations. This paper describes a bottom-up procedure for discovering multivalued dependencies (MVDs) in observed data without knowing `a priori the relationships amongst the attributes. The proposed algorithm is an application of the technique we designed for learning conditional independencies in probabilistic reasoning. A prototype system for automated database schema design has been implemented. Experiments were carried out to demonstrate both the effectiveness and efficiency of our method. 1

In this paper, the feasibility of using finite totally ordered probability models under Aleliunas's Theory of Probabilistic Logic [Aleliunas, 1988] is investigated. The general form of the probability algebra of these models is derived and the number of possible algebras with given size is deduced. Based on this analysis, we discuss problems of denominator-indifference and ambiguity-generation that arise in reasoning by cases and abductive reasoning. An example is given that illustrates how these problems arise. The investigation shows that a finite probability model may be of very limited usage. 1 Introduction This research started from the process of building a medical diagnostic expert system, in the domain of EEG analysis. In this domain we wanted to combine evidence, but the experts consulted claimed that they did not use numbers, but rather used a small number of terms to describe uncertainty. Thus we were lead to a finite non-numerical uncertainty management mechanism. In such ...

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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.