Fusion, propagation, and structuring in belief networks
Artificial Intelligence
Applying inductive learning to enhance knowledge-based expert systems
Decision Support Systems
Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Comments on Approximating Discrete Probability Distributions with Dependence Trees
IEEE Transactions on Pattern Analysis and Machine Intelligence
Probabilistic reasoning in expert systems: theory and algorithms
Probabilistic reasoning in expert systems: theory and algorithms
A Bayesian method for constructing Bayesian belief networks from databases
Proceedings of the seventh conference (1991) on Uncertainty in artificial intelligence
An entropy-based learning algorithm of Bayesian conditional trees
UAI '92 Proceedings of the eighth conference on Uncertainty in Artificial Intelligence
An Information Theoretic Approach to Rule Induction from Databases
IEEE Transactions on Knowledge and Data Engineering
Machine Learning
Simulation Approaches to General Probabilistic Inference on Belief Networks
UAI '89 Proceedings of the Fifth Annual Conference on Uncertainty in Artificial Intelligence
An Empirical Evaluation of a Randomized Algorithm for Probabilistic Inference
UAI '89 Proceedings of the Fifth Annual Conference on Uncertainty in Artificial Intelligence
UAI '89 Proceedings of the Fifth Annual Conference on Uncertainty in Artificial Intelligence
Weighing and Integrating Evidence for Stochastic Simulation in Bayesian Networks
UAI '89 Proceedings of the Fifth Annual Conference on Uncertainty in Artificial Intelligence
an entropy-driven system for construction of probabilistic expert systems from databases
UAI '90 Proceedings of the Sixth Annual Conference on Uncertainty in Artificial Intelligence
A method of computing generalized Bayesian probability values for expert systems
IJCAI'83 Proceedings of the Eighth international joint conference on Artificial intelligence - Volume 1
Approximating discrete probability distributions with dependence trees
IEEE Transactions on Information Theory
A Decision Theory Approach to the Approximation of Discrete Probability Densities
IEEE Transactions on Pattern Analysis and Machine Intelligence
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The representation of uncertainty, and reasoning in the presence of uncertainty, has become an important area of research in expert systems. Belief networks have been found to provide an effective framework for the representation of uncertainty using probability calculus. Unfortunately, belief propagation techniques for general network structures are computationally intense. In this paper, we present belief network representations that approximate the underlying dependency structure in a problem domain in order to allow efficient propagation of beliefs. An important issue then is one of obtaining the 'best' approximate representation. A criterion is required to measure the closeness of the approximate to the actual. We examine desirable features of measures that compare approximate representations to the actual one. We identify two well-known measures, called the logarithm rule and the quadratic rule, as having special properties for evaluating approximations. We present a new result that shows the equivalence of using the logarithm rule to that of finding the maximum likelihood estimator. Next, we discuss the modeling implications of using the logarithm rule and the quadratic rule in terms of the nature of solutions that are obtained, and the computational effort required to obtain such solutions. Finally, we use a decision theoretic approach to compare such solutions using a common frame of reference. A simple decision problem is modelled as a belief network, and the comparison is performed over a wide range of probability distributions and cost functions. Our results suggest that the logarithm rule is very appropriate for evaluating approximate representations.