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The paper introduces SMART, a spectral transfer method for multi-task linear regression that leverages spectral similarity between source and target tasks, relaxing the bounded-difference assumptions of prior transfer learning methods. SMART estimates the target coefficient matrix by incorporating spectral information from a fitted source model via structured regularization, without requiring access to the raw source data. Theoretical analysis provides non-asymptotic error bounds and near-minimax Frobenius error rates, while experiments on simulated and single-cell data demonstrate improved accuracy and robustness.
Transfer learning gets a boost: SMART sidesteps restrictive assumptions and data sharing limitations by transferring spectral information between tasks, leading to improved accuracy and robustness.
Multi-task learning is effective for related applications, but its performance can deteriorate when the target sample size is small. Transfer learning can borrow strength from related studies; yet, many existing methods rely on restrictive bounded-difference assumptions between the source and target models. We propose SMART, a spectral transfer method for multi-task linear regression that instead assumes spectral similarity: the target left and right singular subspaces lie within the corresponding source subspaces and are sparsely aligned with the source singular bases. Such an assumption is natural when studies share latent structures and enables transfer beyond the bounded-difference settings. SMART estimates the target coefficient matrix through structured regularization that incorporates spectral information from a source study. Importantly, it requires only a fitted source model rather than the raw source data, making it useful when data sharing is limited. Although the optimization problem is nonconvex, we develop a practical ADMM-based algorithm. We establish general, non-asymptotic error bounds and a minimax lower bound in the noiseless-source regime. Under additional regularity conditions, these results yield near-minimax Frobenius error rates up to logarithmic factors. Simulations confirm improved estimation accuracy and robustness to negative transfer, and analysis of multi-modal single-cell data demonstrates better predictive performance. The Python implementation of SMART, along with the code to reproduce all experiments in this paper, is publicly available at https://github.com/boxinz17/smart.