Transfer Learning Under High-Dimensional Generalized Linear Models
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...
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| Published in | Journal of the American Statistical Association Vol. 118; no. 544; pp. 2684 - 2697 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
United States
Taylor & Francis
02.10.2023
Taylor & Francis Ltd |
| Subjects | |
| Online Access | Get full text |
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| Abstract | 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
l
1
/
l
2
-estimation error bounds as well as a bound for a prediction error measure. The theoretical analysis shows that when the target and sources 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.
Supplementary materials
for this article are available online. |
|---|---|
| AbstractList | In this work, we study the transfer learning problem under highdimensional 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.In this work, we study the transfer learning problem under highdimensional 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. 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 sources 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. Supplementary materials for this article are available online. In this work, we study the transfer learning problem under highdimensional generalized linear models (GLMs), which aim to improve the fit on data by borrowing information from useful data. Given which sources to transfer, we propose a transfer learning algorithm on GLM, and derive its / -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 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. In this work, we study the transfer learning problem under highdimensional 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 ℓ 1 / ℓ 2 -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. 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 l 1 / l 2 -estimation error bounds as well as a bound for a prediction error measure. The theoretical analysis shows that when the target and sources 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. Supplementary materials for this article are available online. |
| Author | Feng, Yang Tian, Ye |
| Author_xml | – sequence: 1 givenname: Ye surname: Tian fullname: Tian, Ye organization: Department of Statistics, Columbia University – sequence: 2 givenname: Yang orcidid: 0000-0001-7746-7598 surname: Feng fullname: Feng, Yang organization: Department of Biostatistics, School of Global Public Health, New York University |
| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/38562655$$D View this record in MEDLINE/PubMed |
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| Cites_doi | 10.1214/009053606000000281 10.1214/14-AOS1221 10.1111/j.2517-6161.1996.tb02080.x 10.1007/978-1-4899-3242-6 10.1093/biomet/asw065 10.1111/j.1467-9868.2005.00532.x 10.1214/15-EJS1027 10.1287/mnsc.2020.3729 10.1214/21-AOS2102 10.1109/ICDM.2018.00077 10.4018/978-1-60566-766-9.ch011 10.1186/s40537-016-0043-6 10.1016/j.csda.2016.02.015 10.1109/TKDE.2009.191 10.1214/20-AOS1949 10.1214/13-AOS1096 |
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| References | e_1_3_3_6_1 Zheng C. (e_1_3_3_24_1) 2019 Hajiramezanali E. (e_1_3_3_7_1) 2018 e_1_3_3_18_1 Li S. (e_1_3_3_11_1) 2021 Negahban S. (e_1_3_3_14_1) 2009 e_1_3_3_17_1 e_1_3_3_19_1 Hanneke S. (e_1_3_3_8_1) 2020 e_1_3_3_13_1 e_1_3_3_16_1 e_1_3_3_15_1 e_1_3_3_3_1 Hanneke S. (e_1_3_3_9_1) 2020 e_1_3_3_21_1 e_1_3_3_2_1 e_1_3_3_20_1 e_1_3_3_5_1 e_1_3_3_12_1 e_1_3_3_23_1 e_1_3_3_4_1 Li S. (e_1_3_3_10_1) 2020 e_1_3_3_22_1 |
| References_xml | – year: 2020 ident: e_1_3_3_9_1 article-title: On the Value of Target Data in Transfer Learning publication-title: arXiv preprint arXiv:2002.04747 – ident: e_1_3_3_13_1 doi: 10.1214/009053606000000281 – start-page: 1348 volume-title: Advances in Neural Information Processing Systems year: 2009 ident: e_1_3_3_14_1 – ident: e_1_3_3_20_1 doi: 10.1214/14-AOS1221 – year: 2020 ident: e_1_3_3_10_1 article-title: Transfer Learning in Large-Scale Gaussian Graphical Models with False Discovery Rate Control publication-title: arXiv preprint arXiv:2010.11037 – ident: e_1_3_3_18_1 doi: 10.1111/j.2517-6161.1996.tb02080.x – year: 2019 ident: e_1_3_3_24_1 article-title: On Data Enriched Logistic Regression publication-title: arXiv preprint arXiv:1911.06380 – start-page: 31 volume-title: Advances in Neural Information Processing Systems 31 (NIPS 2018) year: 2018 ident: e_1_3_3_7_1 – ident: e_1_3_3_12_1 doi: 10.1007/978-1-4899-3242-6 – ident: e_1_3_3_15_1 doi: 10.1093/biomet/asw065 – year: 2021 ident: e_1_3_3_11_1 article-title: “Transfer Learning for High-Dimensional Linear Regression: Prediction, Estimation and Minimax Optimality publication-title: Journal of the Royal Statistical Society, Series B – ident: e_1_3_3_23_1 doi: 10.1111/j.1467-9868.2005.00532.x – ident: e_1_3_3_5_1 doi: 10.1214/15-EJS1027 – ident: e_1_3_3_2_1 doi: 10.1287/mnsc.2020.3729 – ident: e_1_3_3_17_1 doi: 10.1214/21-AOS2102 – ident: e_1_3_3_21_1 doi: 10.1109/ICDM.2018.00077 – ident: e_1_3_3_19_1 doi: 10.4018/978-1-60566-766-9.ch011 – ident: e_1_3_3_22_1 doi: 10.1186/s40537-016-0043-6 – ident: e_1_3_3_6_1 doi: 10.1016/j.csda.2016.02.015 – year: 2020 ident: e_1_3_3_8_1 article-title: A no-free-lunch Theorem for Multitask Learning publication-title: arXiv preprint arXiv:2006.15785 – ident: e_1_3_3_16_1 doi: 10.1109/TKDE.2009.191 – ident: e_1_3_3_4_1 doi: 10.1214/20-AOS1949 – ident: e_1_3_3_3_1 doi: 10.1214/13-AOS1096 |
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| Snippet | 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... In this work, we study the transfer learning problem under highdimensional generalized linear models (GLMs), which aim to improve the fit on data by borrowing... In this work, we study the transfer learning problem under highdimensional generalized linear models (GLMs), which aim to improve the fit on target data by... In this work, we study the transfer learning problem under highdimensional generalized linear models (GLMs), which aim to improve the fit on target data by... |
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| SubjectTerms | Algorithms Americans artificial intelligence confidence interval Error analysis Generalized linear models High-dimensional inference Lasso Learning Linear analysis linear models Machine learning Negative transfer prediction Sparsity Statistical models Statistics Transfer learning |
| Title | Transfer Learning Under High-Dimensional Generalized Linear Models |
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