A Unified Computational and Theoretical Framework for High-Dimensional Bayesian Additive Models
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We introduce a general framework for estimation and variable selection in high-dimensional Bayesian generalized additive models where the response belongs to the overdispersed exponential family. Our framework subsumes popular models such as binomial regression, Poisson regression, Gaussian regression, and negative binomial regression, and encompasses both canonical and non-canonical link functions. Our method can be implemented with a highly efficient EM algorithm, allowing us to rapidly attain estimates of the significant functions while thresholding out insignificant ones. Under mild regularity conditions, we establish posterior contraction rates and model selection consistency when the number of covariates grows at nearly exponential rate with sample size. We illustrate our method on both synthetic and real data sets.
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