Mathematics Colloquium: Rachel Wang
Topic: Mini-batch Metropolis-Hastings MCMC with Reversible SGLD Proposal
Traditional MCMC algorithms are computationally intensive and do not scale well to large data. In particular, the Metropolis-Hastings (MH) algorithm requires passing over the entire dataset to evaluate the likelihood ratio in each iteration. We propose a general framework for performing MH-MCMC using mini-batches of the whole dataset and show that this gives rise to approximately a tempered stationary distribution. We prove that the algorithm preserves the modes of the original target distribution and derive an error bound on the approximation with mild assumptions on the likelihood. To further extend the utility of the algorithm to high dimensional settings, we construct a proposal with forward and reverse moves using stochastic gradient and show that the construction leads to reasonable acceptance probabilities. We demonstrate the performance of our algorithm in both low dimensional models and high dimensional neural network applications. Particularly in the latter case, compared to popular optimisation methods, our method is more robust to the choice of learning rate and improves testing accuracy.
About the speaker
Professor Rachel Wang (University of Sydney)
Rachel Wang is currently a DECRA Fellow and lecturer in the School of Mathematics and Statistics at the University of Sydney. She received her PhD from UC Berkeley in 2015, then spent two years as a Stein Fellow at Stanford before returning to Sydney. Her research focuses on theory and methods in statistical network modelling and statistical machine learning, with applications to genomics.