Deep Learning for Variable Selection in Nonparametric Spatial Autoregressive Tobit Models

Deep learning is known for its exceptional ability to tackle complex problems and handle large-scale data. Its primary strengths include automatic learning of intricate data representations without the need for manual feature extraction, as well as managing nonlinear relationships and vast datasets. To utilize the advantages of deep learning in capturing complex structural features in feature space, we investigated the variable selection issue in a likelihood-based nonparametric spatial autoregressive Tobit model and introduced the NSTVSNet algorithm. This algorithm combines the sparsity of lasso with the nonlinear approximation capability of neural networks, integrating lasso penalties into residual networks with spatial effects for feature selection. By introducing a set of auxiliary variables, the variable selection problem is transformed into a parameter optimization challenge. Simulation experiments and real-data analyses demonstrated the effectiveness of our approach.