Spike-and-Slab Group Lasso for Consistent Estimation and Variable Selection in Non-Gaussian Generalized Additive Models

We study estimation and variable selection in non-Gaussian Bayesian generalized additive models (GAMs) under a spike-and-slab prior for grouped variables. Our framework subsumes GAMs for logistic regression, Poisson regression, negative binomial regression, and gamma regression, and encompasses both canonical and non-canonical link functions. Under mild conditions, we establish posterior contraction rates and model selection consistency when $p \gg n$. For computation, we propose an EM algorithm for obtaining MAP estimates in our model, which is available in the R package sparseGAM. We illustrate our method on both synthetic and real data sets.