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- BY Z. I. BOTEV, Joseph F. Grotowski, Dirk P. Kroese
- 2010

We present a new adaptive kernel density estimator based on linear diffusion processes. The proposed estimator builds on existing ideas for adaptive smoothing by incorporating information from a pilot density estimate. In addition, we propose a new plug-in bandwidth selection method that is free from the arbitrary normal reference rules used by existing… (More)

- Pieter-Tjerk de Boer, Dirk P. Kroese, Shie Mannor, Reuven Y. Rubinstein
- Annals OR
- 2005

The cross-entropy (CE) method is a new generic approach to combinatorial and multi-extremal optimization and rare event simulation. The purpose of this tutorial is to give a gentle introduction to the CE method. We present the CE methodology, the basic algorithm and its modifications, and discuss applications in combinatorial optimization and machine… (More)

This chapter describes how difficult statistical estimation problems can often be solved efficiently by means of the cross-entropy (CE) method. The CE method can be viewed as an adaptive importance sampling procedure that uses the cross-entropy or Kullback–Leibler divergence as a measure of closeness between two sampling distributions. The CE method is… (More)

In recent years, the cross-entropy method has been successfully applied to a wide range of discrete optimization tasks. In this paper we consider the cross-entropy method in the context of continuous optimization. We demonstrate the effectiveness of the cross-entropy method for solving difficult continuous multi-extremal optimization problems, including… (More)

- Dirk P. Kroese
- 2004

The estimation of P(Sn > u) by simulation, where Sn is the sum of independent, identically distributed random varibles Y1, . . . , Yn, is of importance inmany applications. We propose two simulation estimators based upon the identity P(Sn > u) = nP(Sn > u, Mn = Yn), where Mn = max(Y1, . . . , Yn). One estimator uses importance sampling (for Yn only), and… (More)

- Andre Costa, Owen Dafydd Jones, Dirk P. Kroese
- Oper. Res. Lett.
- 2007

We present new theoretical convergence results on the Cross-Entropy method for discrete optimization. Our primary contribution is to show that a popular implementation of the Cross-Entropy method converges, and finds an optimal solution with probability arbitrarily close to 1. We also give necessary conditions and sufficient conditions under which an… (More)

- Zdravko I. Botev, Dirk P. Kroese
- Proceedings of the 2004 Winter Simulation…
- 2004

Global likelihood maximization is an important aspect of many statistical analyses. Often the likelihood function is highly multi-extremal. This presents a significant challenge to standard search procedures, which often settle too quickly into an inferior local maximum. We present a new approach based on the cross-entropy (CE) method, and illustrate its… (More)

- G. Alon, Dirk P. Kroese, T. Raviv, Reuven Y. Rubinstein
- Annals OR
- 2005

The buffer allocation problem (BAP) is a well-known difficult problem in the design of production lines. We present a stochastic algorithm for solving the BAP, based on the cross-entropy method, a new paradigm for stochastic optimization. The algorithm involves the following iterative steps: (a) the generation of buffer allocations according to a certain… (More)

- Kin-Ping Hui, Nigel Bean, Miro Kraetzl, Dirk P. Kroese
- Annals OR
- 2005

Consider a network of unreliable links, modelling for example a communication network. Estimating the reliability of the network – expressed as the probability that certain nodes in the network are connected – is a computationally difficult task. In this paper we study how the Cross-Entropy method can be used to obtain more efficient network reliability… (More)

- Zdravko I. Botev, Dirk P. Kroese
- Statistics and Computing
- 2012

We describe a new Monte Carlo algorithm for the consistent and unbiased estimation of multidimensional integrals and the efficient sampling from multidimensional densities. The algorithm is inspired by the classical splitting method and can be applied to general static simulation models. We provide examples from rare-event probability estimation, counting,… (More)