Transfer Learning for High-Dimensional Linear Regression: Prediction, Estimation and Minimax Optimality.

Area of Science:

• Statistics
• Machine Learning
• Bioinformatics

Background:

• High-dimensional linear regression presents challenges in estimation and prediction.
• Transfer learning offers a framework to improve model performance by utilizing related auxiliary data.
• Effective knowledge transfer is crucial for enhancing target model accuracy.

Purpose of the Study:

• To develop and analyze methods for high-dimensional linear regression within a transfer learning context.
• To propose an optimal estimator and predictor when informative auxiliary samples are known.
• To introduce a data-driven procedure (Trans-Lasso) for scenarios with unknown informative auxiliary samples.

Main Methods:

• Development of an optimal estimator and predictor for transfer learning with known informative auxiliary samples.
• Proposal of Trans-Lasso, a robust and efficient data-driven transfer learning procedure.
• Validation through numerical studies and application to gene expression data.

Main Results:

• Optimal rates of convergence for estimation and prediction are achieved, outperforming methods without auxiliary data.
• Trans-Lasso demonstrates robustness to non-informative samples and efficiency in knowledge transfer.
• Improved gene expression prediction performance in a target tissue by incorporating auxiliary data from other tissues.

Conclusions:

• Transfer learning significantly enhances high-dimensional linear regression performance by leveraging auxiliary data.
• Trans-Lasso provides an effective and robust approach for knowledge transfer in regression tasks.
• The methodology shows practical utility in biological applications like gene expression analysis.