25: High-dimensional Bayesian regression and classification using discretized hyperpriors

Music City Center 

In Bayesian statistics, various shrinkage priors such as the horseshoe and lasso priors have been widely used for the problem of high-dimensional regression and classification. The type of shrinkage priors is determined by the choice of the distributions for hyperparameters, called hyperpriors. As a result, the posterior sampling method should vary depending on the choice of hyperpriors. To address this issue, we develop a new family of hyperpriors via a notion of discretization. The great merit of our discretization approach is that the full conditional of any hyperparameter always becomes a multinomial distribution. This feature provides a unifying posterior sampling scheme for any choice of hyperpriors. In addition, the proposed discretization approach includes the spike-and-slab prior as a special case. We illustrate the proposed method using several commonly used shrinkage priors such as horseshoe prior, Dirichlet-Laplace prior, and Bayesian lasso prior. We demonstrate the performance of our proposed method through a simulation study and a real data application.

Bayesian shrinkage priors

Discretization

Gibbs sampler

High-dimensional regression and classification 

Section on Bayesian Statistical Science