An adaptive Metropolis-Hastings scheme: sampling and optimization

摘要

We propose an adaptive Metropolis-Hastings algorithm in which sampled dataare used to update the proposal distribution. We use the samples found by thealgorithm at a particular step to form the information-theoretically optimalmean-field approximation to the target distribution, and update the proposaldistribution to be that approximatio. We employ our algorithm to sample theenergy distribution for several spin-glasses and we demonstrate the superiorityof our algorithm to the conventional MH algorithm in sampling and in annealingoptimization.