Fast Algorithms and Theory for High-Dimensional Bayesian Varying Coefficient Models
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Nonparametric varying coefficient (NVC) models are widely used for modeling time-varying effects on responses that are measured repeatedly. In this paper, we introduce the nonparametric varying coefficient spike-and-slab lasso (NVC-SSL) for Bayesian estimation and variable selection in NVC models. The NVC-SSL simultaneously estimates the functionals of the significant time-varying covariates while thresholding out insignificant ones. Our model can be implemented using a highly efficient expectation-maximization (EM) algorithm, thus avoiding the computational burden of Markov chain Monte Carlo (MCMC) in high dimensions. In contrast to frequentist NVC models, hardly anything is known about the large-sample properties for Bayesian NVC models. In this paper, we take a step towards addressing this longstanding gap between methodology and theory by deriving posterior contraction rates under the NVC-SSL model when the number of covariates grows at nearly exponential rate with sample size. Finally, we illustrate our methodology through simulation studies and data analysis.
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