Incremental transfer learning for spatial autoregressive model with linear constraints

Transfer learning is generally regarded as a beneficial technique for utilizing external information to enhance learning performance on target tasks. However, current research on transfer learning in high-dimensional regression models does not take into account both the location information of the data and the explicit utilization of prior knowledge. In the framework of transfer learning, this study seeks to resolve the spatial autoregressive problem and investigate the impact of introducing linear constraints. In this paper, a two-step transfer learning approach and a transferable source detection algorithm based on cross-validation are proposed when the input dimensions of the source and target datasets are the same. When the input dimensions are different, this paper suggests a straightforward and workable incremental transfer learning method. Additionally, for the estimating model developed under this method, Karush–Kuhn–Tucker (KKT) conditions and degrees of freedom are determined, and a Bayesian Information Criterion (BIC) is created for choosing hyperparameters. The effectiveness of the proposed methods is proven by numerical calculations, and the performance of the model in transfer learning estimation is improved by the addition of linear constraints.