Generalized Cross-Entropy Methods
by Dirk Kroese
Abstract: The Cross-Entropy (CE) and Minimum Cross-Entropy (MCE) methods are well-known Monte Carlo techniques for rare-event probability estimation and optimization. The principal distance measure used in both cases is the Kullback-Leibler cross-entropy. In this talk we investigate how the CE and MCE can be extended and generalized to include more general cross-entropy distances. We formulate a generalized cross-entropy framework which subsumes both CE and MCE, and show how in particular the chi square distance yields a viable alternative to Kullback-Leibler distance. The theory is illustrated with various examples in rare-event simulation and optimization. (Joint work with Zdravko Botev and Thomas Taimre).
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