Transfer learning for high dimensional data with discrete responses

Discrete responses are frequently encountered in applications, particularly in classification problems. However, the high cost of collecting responses or labels often leads to a scarcity of samples, which significantly diminishes the accuracy of statistical inferences, particularly in high-dimensional settings. To address this limitation, transfer learning can be utilized for high-dimensional data with discrete responses by incorporating relevant source data into the target study of interest. Within the framework of generalized linear models, the case where responses are bounded are first considered, and an importance-weighted transfer learning method, referred to as IWTL-DR, is proposed. This method selects data at the individual level, thereby utilizing the source data more efficiently. Subsequently, this approach is extended to scenarios involving unbounded responses. Theoretical properties of the IWTL-DR method are established and compared with existing techniques. Extensive simulations and analyses of real data show the advantages of our approach.