Nonparametric spatial autoregressive model using deep neural networks

With the rapid development of social networks, spatial autoregressive models with covariates are increasingly used in practice. We introduce spatial effects into the artificial neural network model and propose a new method for spatial data prediction. Our method is based on artificial neural network, combined with the idea of nonparametric spatial autoregressive model. The spatial lag term is a input of the network, considering the spatial effect of variables. The feature of strong generalization ability of the artificial neural network model is given full play. The simulation results point out that the proposed method has better prediction accuracy than the maximum likelihood method, naive least squares method and B-spline method when the random error term obey non-normal distribution; in the case of spatial effects of the data, the proposed model has significantly improved the prediction effect compared with the common artificial neural network.