Stochastic Gradient Monomial Gamma Sampler
This addresses a bottleneck in Bayesian inference for large datasets, though it appears incremental as an enhancement to existing stochastic gradient MCMC methods.
The paper tackles the problem of poor mixing in stochastic gradient MCMC for multimodal posterior distributions by proposing a framework based on Hamiltonian Monte Carlo with a generalized kinetic function, resulting in improved sampling efficiency as demonstrated in multiple applications.
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.