Adaptive Metropolis Sampling and Optimization with Product Distributions

The Metropolis-Hastings (MH) algorithm is a way to IID sample a provided target distribution π(x). It works by repeatedly sampling a separate proposal distribution T (x, x′) to generate a random walk {x(t)} which converges to a set of samples of π. Here, we introduce a T -updating phase after the cooling period and before sampling begins. In the updating phase, {x(t)} is used to update T at t and our update method corresponds to the information-theoretically optimal meanfield approximation to π. We employ our algorithm to sample the energy distribution for several spin-glasses and we demonstrate the superiority of our algorithm to the conventional MH algorithm. dhw@email.arc.nasa.gov c.lee1@physics.ox.ac.uk