Distributionally Robust Active Learning for Gaussian Process Regression
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arXiv
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| Main Authors: | , , , , , , , , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909676403163136 |
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| author | Takeno, Shion Okura, Yoshito Inatsu, Yu Aoyama, Tatsuya Tanaka, Tomonari Akahane, Satoshi Hanada, Hiroyuki Hashimoto, Noriaki Murayama, Taro Lee, Hanju Kojima, Shinya Takeuchi, Ichiro |
| author_facet | Takeno, Shion Okura, Yoshito Inatsu, Yu Aoyama, Tatsuya Tanaka, Tomonari Akahane, Satoshi Hanada, Hiroyuki Hashimoto, Noriaki Murayama, Taro Lee, Hanju Kojima, Shinya Takeuchi, Ichiro |
| contents | Gaussian process regression (GPR) or kernel ridge regression is a widely used and powerful tool for nonlinear prediction. Therefore, active learning (AL) for GPR, which actively collects data labels to achieve an accurate prediction with fewer data labels, is an important problem. However, existing AL methods do not theoretically guarantee prediction accuracy for target distribution. Furthermore, as discussed in the distributionally robust learning literature, specifying the target distribution is often difficult. Thus, this paper proposes two AL methods that effectively reduce the worst-case expected error for GPR, which is the worst-case expectation in target distribution candidates. We show an upper bound of the worst-case expected squared error, which suggests that the error will be arbitrarily small by a finite number of data labels under mild conditions. Finally, we demonstrate the effectiveness of the proposed methods through synthetic and real-world datasets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_16870 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Distributionally Robust Active Learning for Gaussian Process Regression Takeno, Shion Okura, Yoshito Inatsu, Yu Aoyama, Tatsuya Tanaka, Tomonari Akahane, Satoshi Hanada, Hiroyuki Hashimoto, Noriaki Murayama, Taro Lee, Hanju Kojima, Shinya Takeuchi, Ichiro Machine Learning Gaussian process regression (GPR) or kernel ridge regression is a widely used and powerful tool for nonlinear prediction. Therefore, active learning (AL) for GPR, which actively collects data labels to achieve an accurate prediction with fewer data labels, is an important problem. However, existing AL methods do not theoretically guarantee prediction accuracy for target distribution. Furthermore, as discussed in the distributionally robust learning literature, specifying the target distribution is often difficult. Thus, this paper proposes two AL methods that effectively reduce the worst-case expected error for GPR, which is the worst-case expectation in target distribution candidates. We show an upper bound of the worst-case expected squared error, which suggests that the error will be arbitrarily small by a finite number of data labels under mild conditions. Finally, we demonstrate the effectiveness of the proposed methods through synthetic and real-world datasets. |
| title | Distributionally Robust Active Learning for Gaussian Process Regression |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2502.16870 |