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. 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 (ProbitDA) and Bayesian Logit regression (LogitDA), and Bayesian Lasso Regression (LassoDA). Concretely, for ProbitDA and LogitDA, we…