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A simple approach to Bayesian network computations
, 1994
"... The general problem of computing posterior probabilities in Bayesian networks is NPhard (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 ..."
Abstract

Cited by 82 (8 self)
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The general problem of computing posterior probabilities in Bayesian networks is NPhard (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.
A Computational Theory of Decision Networks
 International Journal of Approximate Reasoning
, 1994
"... 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 decis ..."
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Cited by 33 (2 self)
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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.
Automated Database Schema Design Using Mined Data Dependencies
 J. Amer. Soc. Inform. Sci
, 1998
"... 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 bottomup procedure for d ..."
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Cited by 6 (0 self)
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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 bottomup 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
Sequential Updating Conditional Probability in Bayesian Networks by Posterior Probability
 In Proceedings of the Eighth Biennial Conference of the Canadian Society for Computational Studies of Intelligence
, 1990
"... The Bayesian network is a powerful knowledge representation formalism; it is also capable of improving its precision through experience. Spiegelhalter et al. [1989] proposed a procedure for sequential updating forward conditional probabilities (FCP) in Bayesian networks of diameter 1 with a single p ..."
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Cited by 4 (1 self)
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The Bayesian network is a powerful knowledge representation formalism; it is also capable of improving its precision through experience. Spiegelhalter et al. [1989] proposed a procedure for sequential updating forward conditional probabilities (FCP) in Bayesian networks of diameter 1 with a single parent node. The procedure assumes certainty for each diagnosis which is not practical for many applications. In this paper we present a new algorithm (ALPP) that allows refinement of FCPs based on expert estimates of posterior probability. ALPP applies to any DAG of diameter 1. Fast convergence is achieved. Simulation results compare ALPP with Spiegelhalter’s method. 1
Can Uncertainty Management Be Realized In A Finite Totally Ordered Probability Algebra?
, 1990
"... 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. ..."
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Cited by 2 (0 self)
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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 denominatorindifference and ambiguitygeneration 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 nonnumerical uncertainty management mechanism. In such ...
A simple approach toBayesian network computations
"... The general problem of computing posterior probabilities in Bayesian networks is NPhard (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 ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
The general problem of computing posterior probabilities in Bayesian networks is NPhard (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.
1 Can Uncertainty Management Be Realized In A Finite Totally Ordered Probability Algebra?
"... 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. ..."
Abstract
 Add to MetaCart
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 denominatorindifference and ambiguitygeneration 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