By John G. Webster (Editor)
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Extra resources for 31.Knowledge and Data Engineering
Z. ), Proc. Neural Information Processing Systems, pages 81–90, New York, American Inst. of Physics, 1988. 30. D. Haussler, Generalizing the PAC model: Sample size bounds from metric dimension-based uniform convergence results, in Proc. 30th Annu. Symp. Foundations Comput. , pages 40–45. Computer Society Press, IEEE, 1989. 31. A. R. Barron, Approximation and estimation bounds for artificial neural networks, in Proc. 4th Annual Workshop on Computational Learning Theory (COLT’91), pages 243–249, Palo Alto, CA, Morgan Kaufmann, 1991.
Approximate techniques tend to generate approximate results using user-controlled bounds on the amount of time used to do the inference. The most commonplace are techniques based on Monte Carlo sampling, Gibbs sampling, or logic sampling. The basis of these techniques is to use the belief network as a generator of random samples, check how many times the desired cases show up in the random sample, and from that compute the probabilities of those cases. There are ways of speeding this process up by selecting which sample to create and then discounting the value of the sample.
S p θi, j,k ) = f (s1 θi, j,k ) . . f (s p θi, j,k ) Choose some prior distribution (i, j,k) for i, j,k. The posterior distribution (i, j,k͉s), which is the estimate of i, j,k, is then f p (s θi, j,k )ξ (θi, j,k ) f f p (s θi, j,k )ξ (θi, j,k )dθi, j,k for θi, j,k ∈ which is proportional to f p(s͉i, j,k)(i, j,k). When sampling with replacement from the database D, a standard description of the sample distribution f(sl͉i, j,k) is as a Bernoulli distribution; in a relevant sample, there is a i, j,k chance that the sample will have Xi assigned to xik (given that the parents ⌸i have the assignment i[ j]), and a 1 Ϫ i, j,k chance that Xi will have a different value.
31.Knowledge and Data Engineering by John G. Webster (Editor)