CPSG-MCMC: Clustering-Based Preprocessing method for Stochastic Gradient MCMC

摘要

In recent years, stochastic gradient Markov Chain Monte Carlo (SG-MCMC) methods have been raised to process large-scale dataset by iterative learning from small minibatches. However, the high variance caused by naive subsampling usually slows down the convergence to the desired posterior distribution. In this paper, we propose an effective subsampling strategy to reduce the variance based on a failed attempt to do importance sampling. In particular, before sampling, we partition the dataset with k-means clustering algorithm in a preprocessing step and use the fixed clustering throughout the entire MCMC simulation. Then during simulation, we approximate the gradient of log-posterior via summing the estimated gradient of each cluster. The resulting procedure is surprisingly simple without enhancing the complexity of the original algorithm during sampling procedure. We apply our Clustering-based Preprocessing strategy on stochastic gradient Langevin dynamics, stochastic gradient Hamilton Monte Carlo and stochastic gradient Riemann Langevin dynamics. Empirically, we provide thorough numerical results to back up the effectiveness and efficiency of our approach.