Generalized Cross-entropy Methods with Applications to Rare-event Simulation and Optimization
- 1 November 2007
- journal article
- research article
- Published by SAGE Publications in SIMULATION
- Vol. 83 (11) , 785-806
Abstract
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.Keywords
This publication has 18 references indexed in Scilit:
- A Stochastic Minimum Cross-Entropy Method for Combinatorial Optimization and Rare-event Estimation*Methodology and Computing in Applied Probability, 2005
- The Cross-Entropy Method2004
- Bayesian Data Analysis2003
- Kernel Smoothing1995
- Multivariate Density Estimation1992
- Dual Methods in Entropy Maximization. Application to Some Problems in CrystallographySIAM Journal on Optimization, 1992
- Duality Relationships for Entropy-Like Minimization ProblemsSIAM Journal on Control and Optimization, 1991
- The generalized maximum entropy principleIEEE Transactions on Systems, Man, and Cybernetics, 1989
- Penalty Functions and Duality in Stochastic Programming Via ϕ-Divergence FunctionalsMathematics of Operations Research, 1987
- A comparative study of some kernel-based nonparametric density estimatorsJournal of Statistical Computation and Simulation, 1985