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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2402.11410 |
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| _version_ | 1866929529761562624 |
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| author | Arunachaleswaran, Eshwar Ram Collina, Natalie Roth, Aaron Shi, Mirah |
| author_facet | Arunachaleswaran, Eshwar Ram Collina, Natalie Roth, Aaron Shi, Mirah |
| contents | Blasiok et al. [2023] proposed distance to calibration as a natural measure of calibration error that unlike expected calibration error (ECE) is continuous. Recently, Qiao and Zheng [2024] gave a non-constructive argument establishing the existence of an online predictor that can obtain $O(\sqrt{T})$ distance to calibration in the adversarial setting, which is known to be impossible for ECE. They leave as an open problem finding an explicit, efficient algorithm. We resolve this problem and give an extremely simple, efficient, deterministic algorithm that obtains distance to calibration error at most $2\sqrt{T}+1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_11410 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An Elementary Predictor Obtaining $2\sqrt{T}+1$ Distance to Calibration Arunachaleswaran, Eshwar Ram Collina, Natalie Roth, Aaron Shi, Mirah Machine Learning Data Structures and Algorithms Blasiok et al. [2023] proposed distance to calibration as a natural measure of calibration error that unlike expected calibration error (ECE) is continuous. Recently, Qiao and Zheng [2024] gave a non-constructive argument establishing the existence of an online predictor that can obtain $O(\sqrt{T})$ distance to calibration in the adversarial setting, which is known to be impossible for ECE. They leave as an open problem finding an explicit, efficient algorithm. We resolve this problem and give an extremely simple, efficient, deterministic algorithm that obtains distance to calibration error at most $2\sqrt{T}+1$. |
| title | An Elementary Predictor Obtaining $2\sqrt{T}+1$ Distance to Calibration |
| topic | Machine Learning Data Structures and Algorithms |
| url | https://arxiv.org/abs/2402.11410 |