Exploiting Spike-and-Slab Prior for Variational Estimation of Nonlinear Systems

Identification of nonlinear dynamic systems remains challenging nowadays. Although the nonlinear autoregressive with exogenous input (NARX) model is flexible to describe complex nonlinear behaviors, it is critical to select appropriate model terms to obtain a parsimonious description of the system. In this article, a variational Bayesian (VB) approach to the estimation of NARX systems is developed. A sparsity-inducing prior is introduced for model parameters, and the sparseness can be automatically determined by the weighting factor of such prior. The Bayesian model for the identification problem is constructed, and an iterative model pruning strategy is formulated to remove redundant terms and address the structure selection problem. Instead of the single-point estimation, the model parameters with their uncertainties are jointly estimated under the VB framework. Finally, one numerical example and several benchmark datasets are adopted to illustrate that the developed algorithm can work promisingly.