Transfer learning for high dimensional spatial autoregressive model

Abstract

Transfer learning is a learning process that applies models learned in old domains to new domains by utilizing similarities between data, tasks, or models. At present, transfer learning has been widely applied, such as natural language processing, recommendation systems, drug analysis, etc. Research in statistical models mostly focuses on classic linear models such as classification and regression. It is still unclear how transfer learning affects spatial data. Spatial data is an important type of data and has been a hot research topic in statistics and econometrics in recent years. However, in reality, its collection and labeling are expensive and labor-intensive, and there may not be enough data to train a robust model. Therefore, this article considers using auxiliary sample sets that are different from the target dataset but have some similarity to help us estimate and predict the target model, and specifies criteria for determining similarity. We propose transfer learning algorithms based on spatial autoregressive models, which can transfer knowledge from auxiliary datasets to target models of interest to us. Its performance has been demonstrated in numerical simulations and real housing price datasets.