Statistics > Machine Learning
arXiv:2403.13565 (stat)
[Submitted on 20 Mar 2024 (v1), last revised 25 Nov 2024 (this version, v3)]
Title:AdaTrans: Feature-wise and Sample-wise Adaptive Transfer Learning for High-dimensional Regression
View a PDF of the paper titled AdaTrans: Feature-wise and Sample-wise Adaptive Transfer Learning for High-dimensional Regression, by Zelin He and 3 other authors
View PDFHTML (experimental)Abstract:We consider the transfer learning problem in the high dimensional linear regression setting, where the feature dimension is larger than the sample size. To learn transferable information, which may vary across features or the source samples, we propose an adaptive transfer learning method that can detect and aggregate the feature-wise (F-AdaTrans) or sample-wise (S-AdaTrans) transferable structures. We achieve this by employing a fused-penalty, coupled with weights that can adapt according to the transferable structure. To choose the weight, we propose a theoretically informed, data-driven procedure, enabling F-AdaTrans to selectively fuse the transferable signals with the target while filtering out non-transferable signals, and S-AdaTrans to obtain the optimal combination of information transferred from each source sample. We show that, with appropriately chosen weights, F-AdaTrans achieves a convergence rate close to that of an oracle estimator with a known transferable structure, and S-AdaTrans recovers existing near-minimax optimal rates as a special case. The effectiveness of the proposed method is validated using both simulation and real data, demonstrating favorable performance compared to the existing methods.
| Subjects: | Machine Learning (stat.ML); Machine Learning (cs.LG); Statistics Theory (math.ST); Methodology (stat.ME) |
| Cite as: | arXiv:2403.13565 [stat.ML] |
| (orarXiv:2403.13565v3 [stat.ML] for this version) | |
| https://doi.org/10.48550/arXiv.2403.13565 arXiv-issued DOI via DataCite |
Submission history
From: Zelin He [view email][v1] Wed, 20 Mar 2024 12:58:46 UTC (2,717 KB)
[v2] Mon, 18 Nov 2024 15:30:16 UTC (6,416 KB)
[v3] Mon, 25 Nov 2024 03:05:52 UTC (6,416 KB)
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View a PDF of the paper titled AdaTrans: Feature-wise and Sample-wise Adaptive Transfer Learning for High-dimensional Regression, by Zelin He and 3 other authors
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