Improving Gibbs Sampler Scan Quality with DoGS
This provides a practical tool for researchers and practitioners using Gibbs sampling in fields like computer vision and statistical inference, though it is an incremental improvement over existing methods.
The paper tackled the problem of improving Gibbs sampler efficiency by developing Dobrushin-optimized Gibbs samplers (DoGS), which provide customized variable selection orders and explicit convergence bounds, resulting in consistently higher-quality inferences with significantly smaller sampling budgets across multiple applications.
The pairwise influence matrix of Dobrushin has long been used as an analytical tool to bound the rate of convergence of Gibbs sampling. In this work, we use Dobrushin influence as the basis of a practical tool to certify and efficiently improve the quality of a discrete Gibbs sampler. Our Dobrushin-optimized Gibbs samplers (DoGS) offer customized variable selection orders for a given sampling budget and variable subset of interest, explicit bounds on total variation distance to stationarity, and certifiable improvements over the standard systematic and uniform random scan Gibbs samplers. In our experiments with joint image segmentation and object recognition, Markov chain Monte Carlo maximum likelihood estimation, and Ising model inference, DoGS consistently deliver higher-quality inferences with significantly smaller sampling budgets than standard Gibbs samplers.