A mini-batch Metropolis-Hastings algorithm has an approximately tempered stationary distribution, provably preserves posterior modes, and pairs with a reversible stochastic-gradient proposal for high-dimensional neural network training.
Variational inference: A review for statisticians
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Mini-batch Metropolis-Hastings MCMC with Reversible SGLD Proposal
A mini-batch Metropolis-Hastings algorithm has an approximately tempered stationary distribution, provably preserves posterior modes, and pairs with a reversible stochastic-gradient proposal for high-dimensional neural network training.