Fast sampling methods for Bayesian max-margin models

Wenbo Hu, Jun Zhu, Bo Zhang

Abstract: Highlights • We study the stochastic subgradient MCMC methods for Bayesian max-margin models. • Theoretical analysis shows the approximate detailed balance property of our methods. • Stochastic subsampling and thermostats are used for fast convergence and mixing. • Experiments show the efficiency and accuracy of our methods. Abstract Bayesian max-margin models have shown superiority in various practical applications, such as text categorization, collaborative prediction, social network link prediction and crowdsourcing, and they conjoin the flexibility of Bayesian modeling and predictive strengths of max-margin learning. However, Monte Carlo sampling for these models still remains challenging, especially for applications that involve large-scale datasets. In this paper, we present the stochastic subgradient Hamiltonian Monte Carlo (HMC) methods, which are easy to implement and computationally efficient. We show the approximate detailed balance property of subgradient HMC which reveals a natural and validated generalization of the ordinary HMC. Furthermore, we investigate the variants that use stochastic subsampling and thermostats for better scalability and mixing. Using stochastic subgradient Markov Chain Monte Carlo (MCMC), we efficiently solve the posterior inference task of various Bayesian max-margin models and extensive experimental results demonstrate the effectiveness of our approach.