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Title: Spike-and-slab group lasso meets Bayesian P-splines Authors:  Paul Bach - Humboldt University Berlin (Germany) [presenting]
Nadja Klein - Research Center Trustworthy Data Science and Security (UA Ruhr) and Department of Statistics (Technische Universität Dortmund) (Germany)
Abstract: The Spike-and-Slab Group Lasso (SSGL) is combined with Bayesian P-splines to obtain a powerful Bayesian approach for effect selection and estimation in sparse high-dimensional additive models. The proposed method is able to decide whether a covariate has a linear, a nonlinear or no effect at all on the response. Moreover, it provides accurate effect estimates and valid posterior credible bands for uncertainty quantification. An interesting finding is that the original variant of the SSGL prior is not suitable in the present context because of severe MCMC mixing issues for the binary selection indicators. We attribute these issues to the sharp concentration of the Euclidean norm of the group Lasso distribution when the group dimension is not small and introduce a new variant of the SSGL prior for which MCMC mixing works much better. Another key feature of our approach is a new reparametrization that renders groupwise Gibbs updates extremely efficient. This reparametrization is closely related to the Demmler-Reinsch reparametrization but more applicable as it does not require full-rank design matrices. We compare the selection and estimation performance of the suggested method with that of several competitors in simulations and illustrate the applicability of our method by consideration of a real data example.