Dirk P. Kroese

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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)
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)
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)
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)
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)
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)
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)