Stochastic Quasi-Newton Langevin Monte Carlo

Umut Şimşekli (LTCI, Télécom ParisTech)
February 10, 2017 — 10:30 — "Salle du conseil du L2S"

Abstract

Recently, Stochastic Gradient Markov Chain Monte Carlo (SG-MCMC) methods have been proposed for scaling up Monte Carlo computations to large data problems. Whilst these approaches have proven useful in many applications, vanilla SG-MCMC might suffer from poor mixing rates when random variables exhibit strong couplings under the target densities or big scale differences. In this talk, I will present a novel SG-MCMC method that takes the local geometry into account by using ideas from Quasi-Newton optimization methods. These second order methods directly approximate the inverse Hessian by using a limited history of samples and their gradients. Our method uses dense approximations of the inverse Hessian while keeping the time and memory complexities linear with the dimension of the problem. I will provide formal theoretical analysis where it is shown that the proposed method is asymptotically unbiased and consistent with the posterior expectations. I will finally illustrate the effectiveness of the approach on both synthetic and real datasets. This is a joint work with Roland Badeau, Taylan Cemgil and Gaël Richard. arXiv: https://arxiv.org/abs/1602.03442