Generalized Cross-entropy Methods with Applications to Rare-event Simulation and Optimization

Authors:
Z.I. Botev;D.P. Kroese;T. Taimre
Affiliations:
Department of Mathematics The University of Queensland Brisbane 4072, Australia;Department of Mathematics The University of Queensland Brisbane 4072, Australia;Department of Mathematics The University of Queensland Brisbane 4072, Australia
Venue:
Simulation
Year:
2007

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Abstract

The cross-entropy and minimum cross-entropy methods arewell-known Monte Carlo simulation techniques for rare-eventprobability estimation and optimization. In this paper, weinvestigate how these methods can be eXtended to provide a generalnon-parametric cross-entropy framework based onϕ-divergence distance measures. We show how theX 2 distance, in particular, yields a viablealternative to the Kullback-Leibler distance. The theory isillustrated with various eXamples from density estimation,rare-event simulation and continuous multi-eXtremaloptimization.