Predictive Model Selection Criteria for Bayesian Lasso Regression

Abstract

We consider the Bayesian lasso for regression, which can be interpreted as an L1 norm regularization based on a Bayesian approach when the Laplace or doubleexponential prior distribution is placed on the regression coefficients. A crucial issue is an appropriate choice of the values of hyperparameters included in the prior distributions, which essentially control the sparsity in the estimated model. To choose the values of tuning parameters, we introduce a model selection criterion for evaluating a Bayesian predictive distribution for the Bayesian lasso. Numerical results are presented to illustrate the properties of our sparse Bayesian modeling procedure.

Sparse Bayesian Lasso via a Variable-Coefficient $\ell_1$ Penalty

“…Previous work has circumvented this using either a point mass variational distribution for regression coefficients (Tung et al, 2019), which does not directly allow for uncertainty quantification (without, say, bootstrapping Fu and Knight (2000)), or by thresholding small coefficients (Babacan et al, 2014), which requires setting an arbitrary threshold (She, 2009). Kawano et al (2015) vary the threshold while monitoring information criteria.…”