Transfer Learning for Nonparametric Regression: Non-asymptotic Minimax Analysis and Adaptive Procedure
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910305841315840 |
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| author | Cai, T. Tony Pu, Hongming |
| author_facet | Cai, T. Tony Pu, Hongming |
| contents | Transfer learning for nonparametric regression is considered. We first study the non-asymptotic minimax risk for this problem and develop a novel estimator called the confidence thresholding estimator, which is shown to achieve the minimax optimal risk up to a logarithmic factor. Our results demonstrate two unique phenomena in transfer learning: auto-smoothing and super-acceleration, which differentiate it from nonparametric regression in a traditional setting. We then propose a data-driven algorithm that adaptively achieves the minimax risk up to a logarithmic factor across a wide range of parameter spaces. Simulation studies are conducted to evaluate the numerical performance of the adaptive transfer learning algorithm, and a real-world example is provided to demonstrate the benefits of the proposed method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_12272 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Transfer Learning for Nonparametric Regression: Non-asymptotic Minimax Analysis and Adaptive Procedure Cai, T. Tony Pu, Hongming Machine Learning Transfer learning for nonparametric regression is considered. We first study the non-asymptotic minimax risk for this problem and develop a novel estimator called the confidence thresholding estimator, which is shown to achieve the minimax optimal risk up to a logarithmic factor. Our results demonstrate two unique phenomena in transfer learning: auto-smoothing and super-acceleration, which differentiate it from nonparametric regression in a traditional setting. We then propose a data-driven algorithm that adaptively achieves the minimax risk up to a logarithmic factor across a wide range of parameter spaces. Simulation studies are conducted to evaluate the numerical performance of the adaptive transfer learning algorithm, and a real-world example is provided to demonstrate the benefits of the proposed method. |
| title | Transfer Learning for Nonparametric Regression: Non-asymptotic Minimax Analysis and Adaptive Procedure |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2401.12272 |