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This work studies the problem of transfer learning under the functionallinear regression model framework, which aims to improve the estimation andprediction of the target model by leveraging the information from relatedsource models. We measure the relatedness between target and source modelsusing Reproducing Kernel Hilbert Spaces (RKHS) norm, allowing the type ofinformation being transferred to be interpreted by the structural properties ofthe spaces. Two transfer learning algorithms are proposed: one transfersinformation from source tasks when we know which sources to use, while theother one aggregates multiple transfer learning results from the firstalgorithm to achieve robust transfer learning without prior information aboutthe sources. Furthermore, we establish the optimal convergence rates for theprediction risk in the target model, making the statistical gain via transferlearning mathematically provable. The theoretical analysis of the predictionrisk also provides insights regarding what factors are affecting the transferlearning effect, i.e. what makes source tasks useful to the target task. Wedemonstrate the effectiveness of the proposed transfer learning algorithms onextensive synthetic data as well as real financial data application.

Transfer Learning for Functional Linear Regression with Structural Interpretability