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2001). Principles of data mining. Cambridge, MA: MIT Press. Heckerman, D. (1997). Bayesian networks for data mining. Data Mining and Knowledge Discovery 1, 79-119. Jaynes, E. T. (2003). Probability theory: The logic of science. Cambridge University Press, ISBN: 0521592712. Copyright © 2003, Idea Group Inc. Copying or distributing in print or electronic forms without written permission of Idea Group Inc. is prohibited. , & Tomkins, A. (2001). Recommendation systems: A probabilistic analysis. JCSS: Journal of Computer and System Sciences 63(1): 42–61.

The most well-known procedures for automatic classification are built on expectation maximization. With this technique, a set of class parameters are refined by assigning cases to classes probabilistically, with the probability of each case membership determined by the likelihood vector for it in the current class parameters (Cheeseman & Stutz, 1995). After this likelihood computation, a number of cases are moved to new classes to which they belong with high likelihood. This procedure converges to a local maximum, (i) p(D Copyright © 2003, Idea Group Inc.

GLOBAL GRAPHICAL MODEL CHOICE If we have many variables, their interdependencies can be modeled as a graph with vertices corresponding to the variables. The example in Fgure 3 is from Madigan and Raftery(1994) and shows the dependencies in a data matrix related to heart disease. Of course, a graph of this kind can give a data probability to the data matrix in a way analogous to the calculations in the previous section, although the formulas become rather involved and the number of possible graphs increases dramatically with the number of variables.

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