In this paper we propose a general framework of performing MCMC with only a mini-batch of data. We show by estimating the Metropolis-Hastings ratio with only a mini-batch of data, one is essentially sampling from the true posterior raised to a known temperature. We show by experiments that our method, Mini-batch Tempered MCMC (MINT-MCMC), can efficiently explore multiple modes of a posterior distribution. Based on the Equi-Energy sampler (Kou et al. 2006 ), we developed a new parallel MCMC algorithm based on the Equi-Energy sampler, which enables efficient sampling from high-dimensional multi-modal posteriors with well separated modes.
Li, D. et al. prove that mini-batch Metropolis Hastings produces samples from the true posterior raised to a known temperature REF .
Mini-batch Tempered MCMC
arXiv: Computation
Mathematics