Title: Adaptive MCMC via Combining Local Samplers,
Abstract: 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 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 to sample from
the whole distribution, we combine samples from several chains run in parallel,
each exploring only a few modes. The chains are prioritized based on the 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 resulting 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
algorithm remained competitive with the basic version of NUTS on sampling from
unimodal distributions, while significantly outperformed state-of-the-art
competitors on synthetic multimodal problems as well as on a challenging sensor
localization task.