Selecting the LASSO regularization parameter via Bayesian principles

We investigate the Bayesian interpolation method for estimator selection, and apply it to the problem of regularization parameter selection in Ridge and LASSO regressions. Specifically, the Bayesian interpolation method leads to criteria for choosing the Ridge and LASSO regularizations; the criterion for LASSO is novel. We show that our proposed technique gives comparable and sometimes superior performance compared with other methods like the Generalized Cross Validation (GCV), the extended Akaike Information Criterion (AIC) and the extended Bayesian Information Criterion (BIC).