Title: Stochastic Gradient Monomial Gamma Sampler,
Abstract: Recent advances in stochastic gradient techniques have made it possible to
estimate posterior distributions from large datasets via Markov Chain Monte
Carlo (MCMC). However, when the target posterior is multimodal, mixing
performance is often poor. This results in inadequate exploration of the
posterior distribution. A framework is proposed to improve the sampling
efficiency of stochastic gradient MCMC, based on Hamiltonian Monte Carlo. A
generalized kinetic function is leveraged, delivering superior stationary
mixing, especially for multimodal distributions. Techniques are also discussed
to overcome the practical issues introduced by this generalization. It is shown
that the proposed approach is better at exploring complex multimodal posterior
distributions, as demonstrated on multiple applications and in comparison with
other stochastic gradient MCMC methods.