The Minimum Cross Entropy Method For Rare Event Simulations
نویسندگان
چکیده
This paper describes a new idea of finding the importance sampling density in rare events simulations: the MinxEnt method (shorthand for minimum cross-entropy). Some preliminary results show that the method might be very promising. 1 The minxent program Assume • X = (X1, . . . ,Xn) is a random vector (with values denoted by x); • h is the joint density function of X; • Sj(·) (j = 1, . . . , k) are functions of x; Recall the Kullback-Leibler distance between any two density functions f, h of X: D(f |h) = Ef [
منابع مشابه
A Stochastic Minimum Cross-Entropy Method for Combinatorial Optimization and Rare-event Estimation
We present a new method, called the minimum cross-entropy (MCE) method for approximating the optimal solution of NP-hard combinatorial optimization problems and rare-event probability estimation, which can be viewed as an alternative to the standard cross entropy (CE) method. The MCE method presents a generic adaptive stochastic version of Kullback’s classic MinxEnt method. We discuss its simil...
متن کاملGeneralized Cross-entropy Methods with Applications to Rare-event Simulation and Optimization
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 1-divergence distance measures. We show how the 2 2 distance, in particular, yields a viable alternative to...
متن کاملAdaptive Monte Carlo Methods for Rare Event Simulations
We review two types of adaptive Monte Carlo methods for rare event simulations. These methods are based on importance sampling. The first approach selects importance sampling distributions by minimizing the variance of importance sampling estimator. The second approach selects importance sampling distributions by minimizing the cross entropy to the optimal importance sampling distribution. We a...
متن کاملMinimum Cross-entropy Methods for Rare-event Simulation
In this paper we apply the minimum cross-entropy method (MinxEnt) for estimating rare-event probabilities for the sum of i.i.d. random variables. MinxEnt is an analogy of the Maximum Entropy Principle in the sense that the objective is to minimize a relative (or cross) entropy of a target density h from an unknown density f under suitable constraints. The main idea is to use the solution to thi...
متن کاملGeneralized Cross-Entropy Methods
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 distance in particular yields a viable alternative to Kull...
متن کامل