  Markov chain Monte Carlo (MCMC) methods are widely used in machine learning.
One of the major problems with MCMC is the question of how to design chains
that mix fast over the whole state space; in particular, how to select the
parameters of an MCMC algorithm. Here we take a different approach and,
similarly to parallel MCMC methods, instead of trying to find a single chain
that samples from the whole distribution, we combine samples from several
chains run in parallel, each exploring only parts of the state space (e.g., a
few modes only). The chains are prioritized based on kernel Stein discrepancy,
which provides a good measure of performance locally. The samples from the
independent chains are combined using a novel technique for estimating the
probability of different regions of the sample space. Experimental results
demonstrate that the proposed algorithm may provide significant speedups in
different sampling problems. Most importantly, when combined with the
state-of-the-art NUTS algorithm as the base MCMC sampler, our method remained
competitive with NUTS on sampling from unimodal distributions, while
significantly outperforming state-of-the-art competitors on synthetic
multimodal problems as well as on a challenging sensor localization task.
