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

arXiv 2006.10593 ↗First posted 18 Jun 2020stat.ME stat.MLcited by 89

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Abstract (arXiv)

This paper considers the estimation and prediction of a high-dimensional linear regression in the setting of transfer learning, using samples from the target model as well as auxiliary samples from different but possibly related regression models. When the set of "informative" auxiliary samples is known, an estimator and a predictor are proposed and their optimality is established. The optimal rates of convergence for prediction and estimation are faster than the corresponding rates without using the auxiliary samples. This implies that knowledge from the informative auxiliary samples can be transferred to improve the learning performance of the target problem. In the case that the set of informative auxiliary samples is unknown, we propose a data-driven procedure for transfer learning, called Trans-Lasso, and reveal its robustness to non-informative auxiliary samples and its efficiency in knowledge transfer. The proposed procedures are demonstrated in numerical studies and are applied to a dataset concerning the associations among gene expressions. It is shown that Trans-Lasso leads to improved performance in gene expression prediction in a target tissue by incorporating the data from multiple different tissues as auxiliary samples.

Key facts. Cited by 89 papers in the map (data through 7 Oct 2026). First posted on arXiv 18 Jun 2020.

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Citing papers per year: 2021: 3; 2022: 7; 2023: 13; 2024: 21; 2025: 27; 2026: 18.

89 papers.

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  1. 2021Transfer Learning under High-dimensional Generalized Linear Modelscited by 69
  2. 2022Adaptive and Robust Multi-Task Learningcited by 33
  3. 2022Transfer Learning for Contextual Multi-armed Banditscited by 24
  4. 2021Targeting Underrepresented Populations in Precision Medicine: A Federated Transfer Learning Approachcited by 20
  5. 2024Transfer Learning for Nonparametric Regression: Non-asymptotic Minimax Analysis and Adaptive Procedurecited by 19
  6. 2021Multitask Learning and Bandits via Robust Statisticscited by 11
  7. 2024TransFusion: Covariate-Shift Robust Transfer Learning for High-Dimensional Regressioncited by 11
  8. 2022A Class of Geometric Structures in Transfer Learning: Minimax Bounds and Optimalitycited by 9
  9. 2024Smoothness Adaptive Hypothesis Transfer Learningcited by 8
  10. 2023Optimal Multitask Linear Regression and Contextual Bandits under Sparse Heterogeneitycited by 7
  11. 2023Towards the Theory of Unsupervised Federated Learning: Non-asymptotic Analysis of Federated EM Algorithmscited by 7
  12. 2024Minimax Regret Learning for Data with Heterogeneous Subgroupscited by 7
38 more
  1. 2024Analysing Multi-Task Regression via Random Matrix Theory with Application to Time Series Forecastingcited by 7
  2. 2022Transfer Learning with Uncertainty Quantification: Random Effect Calibration of Source to Target (RECaST)cited by 6
  3. 2023What can we learn from quantum convolutional neural networks?cited by 6
  4. 2024Bridging Data Gaps in Healthcare: A Scoping Review of Transfer Learning in Biomedical Data Analysiscited by 6
  5. 2025Representation Retrieval Learning for Heterogeneous Data Integrationcited by 5
  6. 2023Generalization Performance of Transfer Learning: Overparameterized and Underparameterized Regimescited by 4
  7. 2023Guided Adversarial Robust Transfer Learning with Source Mixingcited by 4
  8. 2024Deep Transfer Learning: Model Framework and Error Analysiscited by 4
  9. 2022Transfer Q-learningcited by 3
  10. 2023Unified Transfer Learning Models in High-Dimensional Linear Regressioncited by 3
  11. 2023Transfer Learning for Kernel-based Regressioncited by 3
  12. 2024Distributionally robust risk evaluation with an isotonic constraintcited by 3
  13. 2024LLM Embeddings Improve Test-time Adaptation to Tabular Y|X-Shiftscited by 3
  14. 2022On Hypothesis Transfer Learning of Functional Linear Modelscited by 2
  15. 2022Transfer learning for tensor Gaussian graphical modelscited by 2
  16. 2023Multi-dimensional domain generalization with low-rank structurescited by 2
  17. 2024AdaTrans: Feature-wise and Sample-wise Adaptive Transfer Learning for High-dimensional Regressioncited by 2
  18. 2024Covariate-Elaborated Robust Partial Information Transfer with Conditional Spike-and-Slab Priorcited by 2
  19. 2024Differentially Private Federated Learning: Servers Trustworthiness, Estimation, and Statistical Inferencecited by 2
  20. 2024Trans-Glasso: A Transfer Learning Approach to Precision Matrix Estimationcited by 2
  21. 2025Fixed-Gaussian Spectral Algorithms: Minimax Optimal Rates for Misspecified Learning and Transfercited by 2
  22. 2025Wasserstein Transfer Learningcited by 2
  23. 2025Transfer Learning for Benign Overfitting in High-Dimensional Linear Regressioncited by 2
  24. 2025Neyman-Pearson Classification under Both Null and Alternative Distributions Shiftcited by 2
  25. 2023The ART of Transfer Learning: An Adaptive and Robust Pipelinecited by 1
  26. 2023Transfer Learning with Random Coefficient Ridge Regressioncited by 1
  27. 2023Heterogeneous Transfer Learning for Building High-Dimensional Generalized Linear Models with Disparate Datasetscited by 1
  28. 2024Transfer Learning for Spatial Autoregressive Models with Application to U.S. Presidential Election Predictioncited by 1
  29. 2024Transfer Learning Under High-Dimensional Graph Convolutional Regression Model for Node Classificationcited by 1
  30. 2024Understanding the Statistical Accuracy-Communication Trade-off in Personalized Federated Learning with Minimax Guaranteescited by 1
  31. 2024Multi-Task Dynamic Pricing in Credit Market with Contextual Informationcited by 1
  32. 2025Learning Pareto manifolds in high dimensions: How can regularization help?cited by 1
  33. 2025SIM-Shapley: A Stable and Computationally Efficient Approach to Shapley Value Approximationcited by 1
  34. 2025Multi-task Learning for Heterogeneous Multi-source Block-Wise Missing Datacited by 1
  35. 2025Late Fusion Multi-task Learning for Semiparametric Inference with Nuisance Parameterscited by 1
  36. 2026Adversarial Drift-Aware Predictive Transfer: Toward Durable Clinical AIcited by 1
  37. 2026Transfer Learning Through Conditional Quantile Matchingcited by 1
  38. 2026Context-Constrained Transfer Learning for Tabular Foundation Models via Data Distillationcited by 1

50 most cited of 89 All 89 (JSON)