2018/03/29 by Zhize Li, Tianyi Zhang, Li, Zhize +4
Computer Science · Mathematics · #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #Gaussian Processes and Bayesian Inference #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Markov Chains and Monte Carlo Methods #Stochastic Gradient Optimization Techniques
paper · pdf · doi:10.48550/arxiv.1803.11159
openalex publication_date 2018/03/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Gradient-based Monte Carlo sampling algorithms, like Langevin dynamics and Hamiltonian Monte Carlo, are important methods for Bayesian inference. In large-scale settings, full-gradients are not affordable and thus stochastic gradients evaluated on mini-batches are used as a replacement. In order to reduce the high variance of noisy stochastic gradients, Dubey et al. [2016] applied the standard variance reduction technique on stochastic gradient Langevin dynamics and obtained both theoretical and experimental improvements. In this paper, we apply the variance reduction tricks on Hamiltonian Monte Carlo and achieve better theoretical convergence results compared with the variance-reduced Langevin dynamics. Moreover, we apply the symmetric splitting scheme in our variance-reduced Hamiltonian Monte Carlo algorithms to further improve the theoretical results. The experimental results are also consistent with the theoretical results. As our experiment shows, variance-reduced Hamiltonian Monte Carlo demonstrates better performance than variance-reduced Langevin dynamics in Bayesian regression and classification tasks on real-world datasets.