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Abstract:
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Spike-and-slab priors have been extensively studied for variable selection, and recently been extended to function selection in generalized additive models (GAMs). Most of the previous works on fitting spike-and-slab GAM relies on Markov chain Monte Carlo (MCMC) algorithms to identify the promising subsets of functions. The computational burden of MCMC makes these models less feasible, especially in high-dimensional setting. Besides, most of the current spike-and-slab GAM consider an “all-in-all-out” approach for function selection, rendering less flexibility to answer if non-linear effects are necessary in the model. We propose Bayesian hierarchical generalized additive models for function selection and prediction. The proposed models employ spike-and-slab priors, mixture normal and mixture double exponential, for smooth and sparse solution. Two EM based algorithms, EM-IWLS and EM-Coordinate Descent, are developed for accelerated computation. Simulation studies and real data analysis demonstrated improved performance against the state-of-art models, mgcv and COSSO. The software implementation of the proposed methods is freely available via the R package BHAM.
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