  We propose a new framework for efficiently sampling from complex probability
distributions using a combination of normalizing flows and elliptical slice
sampling (Murray et al., 2010). The central idea is to learn a diffeomorphism,
through normalizing flows, that maps the non-Gaussian structure of the target
distribution to an approximately Gaussian distribution. We then use the
elliptical slice sampler, an efficient and tuning-free Markov chain Monte Carlo
(MCMC) algorithm, to sample from the transformed distribution. The samples are
then pulled back using the inverse normalizing flow, yielding samples that
approximate the stationary target distribution of interest. Our transport
elliptical slice sampler (TESS) is optimized for modern computer architectures,
where its adaptation mechanism utilizes parallel cores to rapidly run multiple
Markov chains for a few iterations. Numerical demonstrations show that TESS
produces Monte Carlo samples from the target distribution with lower
autocorrelation compared to non-transformed samplers, and demonstrates
significant improvements in efficiency when compared to gradient-based
proposals designed for parallel computer architectures, given a flexible enough
diffeomorphism.
