Cross-Semantic Transfer Learning for High-Dimensional Linear Regression
Abstract
Current transfer learning methods for high-dimensional linear regression assume feature alignment across domains, restricting their applicability to semantically matched features. In many real-world scenarios, however, distinct features in the target and source domains can play similar predictive roles, creating a form of cross-semantic similarity. To leverage this broader transferability, we propose the Cross-Semantic Transfer Learning (CSTL) framework. It captures potential relationships by comparing each target coefficient with all source coefficients through a weighted fusion penalty. The weights are derived from the derivative of the SCAD penalty, effectively approximating an ideal weighting scheme that preserves transferable signals while filtering out source-specific noise. For computational efficiency, we implement CSTL using the Alternating Direction Method of Multipliers (ADMM). Theoretically, we establish that under mild conditions, CSTL achieves the oracle estimator with overwhelming probability. Empirical results from simulations and a real-data application confirm that CSTL outperforms existing methods in both cross-semantic and partial signal similarity settings.
Summary
This paper introduces the Cross-Semantic Transfer Learning (CSTL) framework for high-dimensional linear regression. The core problem addressed is the limitation of existing transfer learning methods that require semantically aligned features across domains. CSTL overcomes this limitation by comparing each target coefficient with all source coefficients using a weighted fusion penalty. The weights are derived from the derivative of the SCAD penalty, which aims to approximate an ideal weighting scheme that preserves transferable signals while filtering out source-specific noise. The authors implement CSTL using the Alternating Direction Method of Multipliers (ADMM) for computational efficiency. The key findings include theoretical guarantees demonstrating that CSTL achieves the oracle estimator with overwhelming probability under mild conditions. Empirical results from simulations and a real-data application validate that CSTL outperforms existing methods in both cross-semantic and partial signal similarity settings. This work matters to the field because it expands the applicability of transfer learning to scenarios where feature alignment is not present, a common occurrence in real-world datasets. By enabling the transfer of knowledge between semantically distinct features, CSTL unlocks richer information from source domains, leading to improved estimation and prediction in target tasks.
Key Insights
- •CSTL introduces a novel weighted fusion penalty applied to all possible target-source coefficient pairs, enabling transfer learning even when features are not semantically aligned.
- •The paper establishes the oracle property of CSTL, showing that it achieves the performance of an ideal estimator with known model structure.
- •Data-driven weights, constructed from the derivative of the SCAD penalty, approximate the ideal weighting scheme, allowing practical implementation of CSTL.
- •Simulations demonstrate that CSTL consistently outperforms existing methods like TransLasso and TransGLM, especially in cross-semantic and partial signal similarity settings. CSTL's error remains relatively constant as the degree of cross-semantic similarity increases, unlike competing methods.
- •In a real-data application on the Communities and Crime dataset, CSTL significantly outperforms benchmarks, while TransLasso and TransGLM exhibit negative transfer due to the violation of the feature alignment assumption.
- •The ADMM algorithm provides an efficient computational approach to solve the CSTL optimization problem.
- •A limitation is the reliance on initial estimators (obtained via Lasso) for weight construction. The performance of CSTL depends on the quality of these initial estimates.
Practical Implications
- •CSTL can be applied to a wide range of real-world problems where feature alignment is not guaranteed, such as medical studies, multi-source integration, cross-platform studies, and federated analysis.
- •Researchers and practitioners can use CSTL to improve the accuracy of predictive models in data-scarce target domains by leveraging knowledge from related, data-rich source domains, even when the features have different semantic meanings.
- •Engineers can implement CSTL using the provided ADMM algorithm and data-driven weight selection scheme.
- •Future research directions include extending CSTL to other types of models (e.g., generalized linear models, non-parametric models) and exploring alternative weight selection methods that are less sensitive to the initial estimators. Another direction is developing adaptive methods for choosing the regularization parameters λ0 and λ1.