Model-Averaged [Formula: see text] Regularization using Markov Chain Monte Carlo Model Composition

J Stat Comput Simul. 2015;85(6):1090-1101. doi: 10.1080/00949655.2013.861839.


Bayesian Model Averaging (BMA) is an effective technique for addressing model uncertainty in variable selection problems. However, current BMA approaches have computational difficulty dealing with data in which there are many more measurements (variables) than samples. This paper presents a method for combining [Formula: see text] regularization and Markov chain Monte Carlo model composition techniques for BMA. By treating the [Formula: see text] regularization path as a model space, we propose a method to resolve the model uncertainty issues arising in model averaging from solution path point selection. We show that this method is computationally and empirically effective for regression and classification in high-dimensional datasets. We apply our technique in simulations, as well as to some applications that arise in genomics.

Keywords: MCMCMC; Markov chains; high-dimensional; lasso; model averaging; model composition; variable selection; ℓ1 regularization.