Generalized cross-entropy methods with applications to rare-event simulation and optimization

ZI Botev, DP Kroese, T Taimre - Simulation, 2007 - journals.sagepub.com
Simulation, 2007journals.sagepub.com
The cross-entropy and minimum cross-entropy methods are well-known Monte Carlo
simulation techniques for rare-event probability estimation and optimization. In this paper,
we investigate how these methods can be eXtended to provide a general non-parametric
cross-entropy framework based on φ-divergence distance measures. We show how the χ 2
distance, in particular, yields a viable alternative to the Kullback—Leibler distance. The
theory is illustrated with various eXamples from density estimation, rare-event simulation …
The cross-entropy and minimum cross-entropy methods are well-known Monte Carlo simulation techniques for rare-event probability estimation and optimization. In this paper, we investigate how these methods can be eXtended to provide a general non-parametric cross-entropy framework based on φ-divergence distance measures. We show how the χ2 distance, in particular, yields a viable alternative to the Kullback—Leibler distance. The theory is illustrated with various eXamples from density estimation, rare-event simulation and continuous multi-eXtremal optimization.
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