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The variance of the performance values places another degree of freedom in the performance ordering, which can change the ordering when the variance changes. Consequently, the ordering may change when a baseline with a small variance is changed to one with a large variance (or vice versa). This happens even for normalization methods that do not have anomalies when hypotheses are ordered by their mean values, such as the geometric mean. In short, anomalies in performance ordering will not happen when hypotheses are ranked by their probabilities of mean and when the baseline hypothesis is fixed, such as the case when the median performance of the hypotheses is used as the baseline.
There are several influences on the accuracy of belief network learning. One is that the standard belief network framework requires variables to be discrete. Any naturally continuous variable, such as weight or age, is made discrete in this approach. The more coarse the discretization, the larger the source of error. The finer the discretization, the greater the complexity of the learning problem. Two ways to address this problem are to learn networks that can include continuous variables in the form of conditional Gaussians [Lauritzen (27)], and to improve the way discretization is done [Kozlov and Koller (28)].
S. F. Smith, Flexible learning of problem solving heuristics through adaptive search, in Proc. Int’l Joint Conf. on Artificial Intelligence, pages 422–5. Morgan Kaufman, 1983. 21. J. H. Holland, Properties of the bucket brigade algorithm, in J. J. ), Proc. Int’l. Conf. Genetic Algorithms and Their Applications, pages 1–7, The Robotics Inst. , Pittsburgh, PA, 1985. 22. J. J. Grefenstette, Credit assignment in rule discovery systems based on genetic algorithms, Machine Learning, 3 (2/3): 225–246, October 1988.
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