Variable selection for nonparametric spatial additive autoregressive model via deep learning

In this paper, the variable selection method based on deep neural networks is extended to the nonparametric spatial additive autoregressive model. We introduce the concept of the Lasso penalty, which is established in the spatial residual network structure, and then transform the problem into a constrained optimization. This method can simultaneously perform the processes of variable selection and parameter estimation. Without specifying the degree of sparsity, we are also able to obtain a particular set of selected variables. The model with the nonparametric endogenous effect is used to adapt spatial data uniformly, and the variable selection method is also appropriate for linear cases due to the nonparametric additive covariate structure. The network structure can learn about the specific form of influence of each important feature, so it has good interpretability and can solve the black box problem in deep learning models to some degree. Through simulation studies and analysis of real dataset, the superiority of the method in variable selection and prediction performance is demonstrated.