Transfer Learning for Spatial Autoregressive Models with Missing Responses

Transfer learning is a machine learning approach that enhances target domain performance by leveraging knowledge from source domains. Although this method has been widely applied in regression problems, research remains limited for scenarios involving partially missing response data in the target domain. This study addresses the dual challenges of missing responses and small sample sizes in spatially dependent regression problems by proposing an EM algorithm-based transfer learning framework. The framework first employs the EM algorithm to handle missing responses in spatial autoregressive models, then develops a two-step transfer learning method for known source domains, along with a cross-validation-based detection algorithm for unknown transferable sources. Numerical simulations demonstrate that the proposed methods exhibit superior performance in both parameter estimation accuracy and model robustness.