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Extra info for 31.Knowledge and Data Engineering
In a belief network, all the data describing cars with different colors would essentially be grouped together and treated as if the color variable does not exist. This effectively reduces the size of the distribution that must be learned. Continuing this example, if only 20 of the 100 variables are needed to describe the most complicated interesting events, then the size reduces to about 1020 probabilities to model. The total size of the distribution, however, is not a good indicator of how many data are needed to cover it.
V. N. Vapnik and A. Ya. Chervonenkis, On the uniform convergence of relative frequencies of events to their probabilities, Theoretical Probability and its Applications, XVI (2): 264–280, 1971. 26. N. Sauer, On the density of families of sets, J. Combinatorial Theory (A), 13: 145–147, 1972. 27. A. , Classifying learnable geometric concepts with the Vapnik-Chervonenkis dimension. In Proc. 18th Symp. on Theory of Computing, pages 273–282. ACM, 1986. 28. A. , A general lower bound on the number of examples needed for learning.
In part, it is also because graphical probability models have seen a dramatic resurgence of interest since the late 1980s. GRAPHICAL PROBABILISTIC MODELS Graphical probability models include belief networks, Bayes networks, Markov networks, influence diagrams, similarity diagrams, and others. An excellent overview of many of these different approaches can be found in Buntine (2). Beliefs are typically represented as a set of potentially stochastic variables that interact with one another. Variables represent factors that can influence other factors in the network, or the outcome of a decision or an event.