Extended Stochastic Gradient MCMC for Large-Scale Bayesian Variable Selection
This addresses the challenge of applying Bayesian methods to large-scale computing problems, such as those with variable dimensions or missing data, making it more practical for big data applications.
The paper tackles the limitation of stochastic gradient MCMC algorithms to fixed-dimension, differentiable problems by proposing an extended algorithm that uses latent variables to handle dimension jumping and missing data, resulting in high scalability and significantly greater efficiency than traditional MCMC methods.
Stochastic gradient Markov chain Monte Carlo (MCMC) algorithms have received much attention in Bayesian computing for big data problems, but they are only applicable to a small class of problems for which the parameter space has a fixed dimension and the log-posterior density is differentiable with respect to the parameters. This paper proposes an extended stochastic gradient MCMC lgoriathm which, by introducing appropriate latent variables, can be applied to more general large-scale Bayesian computing problems, such as those involving dimension jumping and missing data. Numerical studies show that the proposed algorithm is highly scalable and much more efficient than traditional MCMC algorithms. The proposed algorithms have much alleviated the pain of Bayesian methods in big data computing.