Transfer Learning for Benign Overfitting in High-Dimensional Linear Regression
This work addresses a gap in combining transfer learning with overparameterized models for practitioners in high-dimensional regression, though it is incremental as it builds on existing MNI frameworks.
The paper tackles the unexplored intersection of transfer learning and benign overfitting in high-dimensional linear regression by proposing a Transfer MNI approach, showing it outperforms target-only methods under certain conditions and demonstrating robustness in experiments.
Transfer learning is a key component of modern machine learning, enhancing the performance of target tasks by leveraging diverse data sources. Simultaneously, overparameterized models such as the minimum-$\ell_2$-norm interpolator (MNI) in high-dimensional linear regression have garnered significant attention for their remarkable generalization capabilities, a property known as benign overfitting. Despite their individual importance, the intersection of transfer learning and MNI remains largely unexplored. Our research bridges this gap by proposing a novel two-step Transfer MNI approach and analyzing its trade-offs. We characterize its non-asymptotic excess risk and identify conditions under which it outperforms the target-only MNI. Our analysis reveals free-lunch covariate shift regimes, where leveraging heterogeneous data yields the benefit of knowledge transfer at limited cost. To operationalize our findings, we develop a data-driven procedure to detect informative sources and introduce an ensemble method incorporating multiple informative Transfer MNIs. Finite-sample experiments demonstrate the robustness of our methods to model and data heterogeneity, confirming their advantage.