Variational inferences for partially linear additive models with variable selection

This article develops a mean field variational Bayes approximation algorithm for posterior inferences of the recently proposed partially linear additive models with simultaneous and automatic variable selection and linear/nonlinear component identification abilities. To solve the problem induced by some complicated expectation evaluations, we proposed two approximations based on Monte Carlo method and Laplace approximation respectively. With high accuracy, the algorithm we derived is much more computationally efficient than the existing Markov Chain Monte Carlo (MCMC) method. The simulation examples are used to demonstrate the performance of our new algorithm versus MCMC. The proposed approach is further illustrated on a real dataset.