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Transfer Learning under High-dimensional Generalized Linear Models

arXiv 2105.14328 ↗First posted 29 May 2021stat.ML cs.LG stat.MEcited by 69

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Abstract (arXiv)

In this work, we study the transfer learning problem under high-dimensional generalized linear models (GLMs), which aim to improve the fit on target data by borrowing information from useful source data. Given which sources to transfer, we propose a transfer learning algorithm on GLM, and derive its ℓ1/ℓ2-estimation error bounds as well as a bound for a prediction error measure. The theoretical analysis shows that when the target and source are sufficiently close to each other, these bounds could be improved over those of the classical penalized estimator using only target data under mild conditions. When we don't know which sources to transfer, an algorithm-free transferable source detection approach is introduced to detect informative sources. The detection consistency is proved under the high-dimensional GLM transfer learning setting. We also propose an algorithm to construct confidence intervals of each coefficient component, and the corresponding theories are provided. Extensive simulations and a real-data experiment verify the effectiveness of our algorithms. We implement the proposed GLM transfer learning algorithms in a new R package glmtrans, which is available on CRAN.

Key facts. Cited by 69 papers in the map (data through 7 Oct 2026). Builds on 11 of its 47 references that are in the map. First posted on arXiv 29 May 2021.

Builds on

11 of 47 references.

References · 11

  1. 2020Transfer Learning for High-dimensional Linear Regression: Prediction, Estimation, and Minimax Optimalitycited by 89
  2. 2013Regularized M-estimators with nonconvexity: Statistical and algorithmic theory for local optimacited by 66
  3. 2019Transfer Learning for Nonparametric Classification: Minimax Rate and Adaptive Classifiercited by 64
  4. 2020On the Value of Target Data in Transfer Learningcited by 62
  5. 2020Transfer Learning in Large-scale Gaussian Graphical Models with False Discovery Rate Controlcited by 38
  6. 2020A No-Free-Lunch Theorem for MultiTask Learningcited by 28
  7. 2018Predicting with Proxies: Transfer Learning in High Dimensioncited by 24
  8. 2013Concentration in unbounded metric spaces and algorithmic stabilitycited by 21
  9. 2018Bayesian multi-domain learning for cancer subtype discovery from next-generation sequencing count datacited by 10
  10. 2013Data enriched linear regressioncited by 7
  11. 2015Regression modeling on stratified data with the lassocited by 5

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 2; 2022: 7; 2023: 12; 2024: 12; 2025: 20; 2026: 16.

69 papers.

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  1. 2023Prediction-Powered Inferencecited by 214
  2. 2022Adaptive and Robust Multi-Task Learningcited by 33
  3. 2021Targeting Underrepresented Populations in Precision Medicine: A Federated Transfer Learning Approachcited by 20
  4. 2021Multitask Learning and Bandits via Robust Statisticscited by 11
  5. 2024TransFusion: Covariate-Shift Robust Transfer Learning for High-Dimensional Regressioncited by 11
  6. 2022A Class of Geometric Structures in Transfer Learning: Minimax Bounds and Optimalitycited by 9
  7. 2024Smoothness Adaptive Hypothesis Transfer Learningcited by 8
  8. 2023Optimal Multitask Linear Regression and Contextual Bandits under Sparse Heterogeneitycited by 7
  9. 2022Transfer Learning with Uncertainty Quantification: Random Effect Calibration of Source to Target (RECaST)cited by 6
  10. 2023Efficient and Multiply Robust Risk Estimation under General Forms of Dataset Shiftcited by 5
  11. 2025Representation Retrieval Learning for Heterogeneous Data Integrationcited by 5
  12. 2023Generalization Performance of Transfer Learning: Overparameterized and Underparameterized Regimescited by 4
38 more
  1. 2023Guided Adversarial Robust Transfer Learning with Source Mixingcited by 4
  2. 2023Unified Transfer Learning Models in High-Dimensional Linear Regressioncited by 3
  3. 2023Transfer Learning for Kernel-based Regressioncited by 3
  4. 2024Distributionally robust risk evaluation with an isotonic constraintcited by 3
  5. 2024LLM Embeddings Improve Test-time Adaptation to Tabular Y|X-Shiftscited by 3
  6. 2022On Hypothesis Transfer Learning of Functional Linear Modelscited by 2
  7. 2022Transfer learning for tensor Gaussian graphical modelscited by 2
  8. 2023Multi-dimensional domain generalization with low-rank structurescited by 2
  9. 2024AdaTrans: Feature-wise and Sample-wise Adaptive Transfer Learning for High-dimensional Regressioncited by 2
  10. 2024Covariate-Elaborated Robust Partial Information Transfer with Conditional Spike-and-Slab Priorcited by 2
  11. 2024Trans-Glasso: A Transfer Learning Approach to Precision Matrix Estimationcited by 2
  12. 2025Fixed-Gaussian Spectral Algorithms: Minimax Optimal Rates for Misspecified Learning and Transfercited by 2
  13. 2025Wasserstein Transfer Learningcited by 2
  14. 2025Transfer Learning for Benign Overfitting in High-Dimensional Linear Regressioncited by 2
  15. 2023The ART of Transfer Learning: An Adaptive and Robust Pipelinecited by 1
  16. 2023Heterogeneous Transfer Learning for Building High-Dimensional Generalized Linear Models with Disparate Datasetscited by 1
  17. 2024Transfer Learning for Spatial Autoregressive Models with Application to U.S. Presidential Election Predictioncited by 1
  18. 2024Transfer Learning Under High-Dimensional Graph Convolutional Regression Model for Node Classificationcited by 1
  19. 2025Multi-task Learning for Heterogeneous Multi-source Block-Wise Missing Datacited by 1
  20. 2025Late Fusion Multi-task Learning for Semiparametric Inference with Nuisance Parameterscited by 1
  21. 2026Adversarial Drift-Aware Predictive Transfer: Toward Durable Clinical AIcited by 1
  22. 2026Transfer Learning Through Conditional Quantile Matchingcited by 1
  23. 2026Context-Constrained Transfer Learning for Tabular Foundation Models via Data Distillationcited by 1
  24. 2022A Correlation-Ratio Transfer Learning and Variational Stein's Paradoxcited by 0
  25. 2022Penalised regression with multiple sources of prior effectscited by 0
  26. 2023Adaptive Lasso, Transfer Lasso, and Beyond: An Asymptotic Perspectivecited by 0
  27. 2023Structural transfer learning of non-Gaussian DAGcited by 0
  28. 2024Fusing Individualized Treatment Rules Using Secondary Outcomescited by 0
  29. 2024An adaptive transfer learning perspective on classification in non-stationary environmentscited by 0
  30. 2024Transfer Learning in ℓ1 Regularized Regression: Hyperparameter Selection Strategy based on Sharp Asymptotic Analysiscited by 0
  31. 2025Transfer Learning through Enhanced Sufficient Representation: Enriching Source Domain Knowledge with Target Datacited by 0
  32. 2025Sparse Optimization for Transfer Learning: A L0-Regularized Framework for Multi-Source Domain Adaptationcited by 0
  33. 2025Transfer Learning for High-dimensional Reduced Rank Time Series Modelscited by 0
  34. 2025Post-Transfer Learning Statistical Inference in High-Dimensional Regressioncited by 0
  35. 2025GeoERM: Geometry-Aware Multi-Task Representation Learning on Riemannian Manifoldscited by 0
  36. 2025Boosting Statistic Learning with Synthetic Data from Pretrained Large Modelscited by 0
  37. 2025High-Dimensional Importance-Weighted Information Criteria: Theory and Optimalitycited by 0
  38. 2025Coefficient Shape Transfer Learning for Functional Linear Regressioncited by 0

50 most cited of 69 All 69 (JSON)