Fast Mixing of Data Augmentation Algorithms: Bayesian Probit, Logit, and Lasso Regression
数据增强算法的快速混合:贝叶斯Probit、Logit与Lasso回归
We propose using a modified conductance-based method to study the mixing time of an important class of two-block Gibbs samplers, the data augmentation (DA) algorithm. %, which is of prominent interest in both theoretical and empirical research. Using this method, we prove the first non-asymptotic polynomial upper bounds on mixing times of three important DA algorithms: DA algorithms for Bayesian Probit regression (Albert and Chib, 1993, ProbitDA) and Bayesian Logit…