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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 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)

- Z I Botev, J F Grotowski, D P Kroese
- 2010

We present a new adaptive kernel density estimator based on linear diffusion processes. The proposed estimator builds on existing ideas for adap-tive 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 RESTART method is a widely applicable simulation technique for the estimation of rare event probabilities. The method is based on the idea to restart the simulation in certain system states, in order to generate more occurrences of the rare event. One of the main questions for any RESTART implementation is how and when to restart the simulation, in… (More)

The two-node tandem Jackson network serves as a convenient reference model for the analysis and testing of different methodologies and techniques in rare event simulation. In this paper we consider a new approach to efficiently estimate the probability that the content of the second buffer exceeds some high level <i>L</i> before it becomes empty, starting… (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)

We apply the cross-entropy (CE) method to problems in clustering and vector quantization. The CE algorithm involves the following iterative steps: (a) the generation of clusters according to a certain para-metric probability distribution, (b) updating the parameters of this distribution according to the Kullback-Leibler cross-entropy. Through various… (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)

I n this paper, we propose a fast adaptive importance sampling method for the efficient simulation of buffer overflow probabilities in queueing networks. The method comprises three stages. First, we estimate the minimum cross-entropy tilting parameter for a small buffer level; next, we use this as a starting value for the estimation of the optimal tilting… (More)

We consider the following continuous polling system: Customers arrive according to a homogeneous Poisson process (or a more general stationary point process) and wait on a circle in order to be served by a single server. The server is " greedy " , in the sense that he always moves (with constant speed) towards the nearest customer. The customers are served… (More)