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DOI: 10.1177/0037549707087067 © 2007 Simulation Councils Inc. Generalized Cross-entropy Methods with Applications to Rare-event Simulation and OptimizationDepartment of Mathematics The University of Queensland Brisbane 4072, Australia botev{at}maths.uq.edu.au
Department of Mathematics The University of Queensland Brisbane 4072, Australia
Department of Mathematics The University of Queensland Brisbane 4072, Australia
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
Key Words: generalized cross-entropy maXimum entropy method cross-entropy method rare-event simulation stochastic optimization Csisár's
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-divergence distance measures. We show how the
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 and continuous multi-eXtremal optimization.