Approximate Posterior Model Probabilities in Additive Models via the Group LASSO

The literature is replete with variable selection techniques for the classical linear regression model. It is only relatively recently that authors have begun to explore variable selection in fully nonparametric and additive regression models. One such variable selection technique is a generalization of the LASSO called the group LASSO. In this work, we demonstrate a connection between the group LASSO and Bayesian inference in additive models with a multivariate Laplace prior for model parameters similar to the connection between the LASSO and Bayesian inference in the linear model with a univariate Laplace prior for regression coefficients. We use this connection to derive approximate posterior model probabilities for additive models. We use the concept of regular and nonregular models to reduce the size of the model space and avoid costly computations.