An Adaptive Transfer Learning Framework for Functional Classification

In this article, we study the transfer learning problem in functional classification, aiming to improve the classification accuracy of the target data by leveraging information from related source datasets. To facilitate transfer learning, we propose a novel transferability function tailored for classification problems, enabling a more accurate evaluation of the similarity between source and target dataset distributions. Interestingly, we find that a source dataset can offer more substantial benefits under certain conditions than another dataset with an identical distribution to the target dataset. This observation renders the commonly-used debiasing step in the parameter-based transfer learning algorithm unnecessary under some circumstances to the classification problem. In particular, we propose two adaptive transfer learning algorithms based on the functional Distance Weighted Discrimination (DWD) classifier for scenarios with and without prior knowledge regarding informative sources. Furthermore, we establish the upper bound on the excess risk of the proposed classifiers, providing the statistical gain via transfer learning mathematically provable. Simulation studies are conducted to thoroughly examine the finite-sample performance of the proposed algorithms. Finally, we implement the proposed method to Beijing air-quality data, and significantly improve the prediction of the PM 2.5 level of a target station by effectively incorporating information from source datasets. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.