  Gibbs sampling is a Markov chain Monte Carlo method that is often used for
learning and inference on graphical models. Minibatching, in which a small
random subset of the graph is used at each iteration, can help make Gibbs
sampling scale to large graphical models by reducing its computational cost. In
this paper, we propose a new auxiliary-variable minibatched Gibbs sampling
method, {\it Poisson-minibatching Gibbs}, which both produces unbiased samples
and has a theoretical guarantee on its convergence rate. In comparison to
previous minibatched Gibbs algorithms, Poisson-minibatching Gibbs supports fast
sampling from continuous state spaces and avoids the need for a
Metropolis-Hastings correction on discrete state spaces. We demonstrate the
effectiveness of our method on multiple applications and in comparison with
both plain Gibbs and previous minibatched methods.
