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Adaptive Monte Carlo Methods for Simulation and Optimization

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When using Monte Carlo methods, it is of interest to adapt the proposal density to obtain faster convergence and more accurate estimation. In order to adapt the proposal, a Cross Entropy criterion is proposed, with some adaptive strategies based on Stochastic Approximation. A novel adaptive population MCMC algorithm is addressed. And how to use a mixture of distribution as proposal is also discussed. Moreover, these adaptations are also suitable for Importance Sampling.

These adaptive Monte Carlo methods are able to be optimization approaches by using some annealing scheme. To show the advantages, they are compared with related methods, e.g. Simulated Annealing.

For Bayesian Inference, a reversible jump version of adaptive Monte Carlo method is proposed to perform parameter estimation/optimization and model selection simultaneously. Variational method with above adaptive strategies forms another approach for approximating inference and learning under Bayesian model.

This talk is part of the Inference Group series.

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