High-dimensional feature selection arises in many areas of modern sciences.For example, in genomic research we want to find the genes that can be used toseparate tissues of different classes (eg. cancer and normal) from tens ofthousands of genes that are active (expressed) in certain tissue cells. To thisend, we wish to fit regression and classification models with a large number offeatures (also called variables, predictors), which is still a tremendouschallenge to date. In the past few years, penalized likelihood methods forfitting regression models based on hyper-lasso penalization have been exploredconsiderably in the literature. However, fully Bayesian methods that use Markovchain Monte Carlo (MCMC) for fitting regression and classification models withhyper-lasso priors are still lack of investigation. In this paper, we introducea new class of methods for fitting Bayesian logistic regression models withhyper-lasso priors using Hamiltonian Monte Carlo in restricted Gibbs samplingframework. We call our methods BLRHL for short. We use simulation studies totest BLRHL by comparing to LASSO, and to investigate the problems of choosingheaviness and scale in BLRHL. The main findings are that the choice ofheaviness of prior plays a critical role in BLRHL, and that BLRHL is relativelyrobust to the choice of prior scale. We further demonstrate and investigateBLRHL in an application to a real microarray data set related to prostatecancer, which confirms the previous findings. An R add-on package called BLRHLwill be available from http://math.usask.ca/~longhai/software/BLRHL.
展开▼
