A0522
Title: Creating manifold structures to accelerate MCMC sampling
Authors: Alexandre Thiery - National University of Singapore (Singapore) [presenting]
Abstract: Consider the observation $y = F(x) +$ (noise) of a quantity of interest $x$. In Bayesian inverse problems, the quantity $x$ typically represents the high-dimensional discretization of a continuous and unobserved field while the evaluations of the forward operator $F$ involve solving a system of partial differential equations. In the low-noise regime, the posterior distribution concentrates in the neighborhood of a nonlinear manifold. As a result, the efficiency of standard MCMC algorithms deteriorates due to the need to take increasingly smaller steps. We present a constrained HMC algorithm that is robust in the low noise regime. Taking the observations generated by the model to be constraints on the prior, we define a manifold on which the constrained HMC algorithm generates samples. By exploiting the geometry of the manifold, our algorithm is able to take larger step sizes than more standard MCMC methods, resulting in a more efficient sampler. If time permits, we will explain how this idea can be extended to classification problems, by exploiting an auxiliary manifold.
