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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Online-Zugang: | https://arxiv.org/abs/2503.02384 |
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| _version_ | 1866917944795070464 |
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| author | Qiao, Mingda Zhao, Eric |
| author_facet | Qiao, Mingda Zhao, Eric |
| contents | Calibration measures quantify how much a forecaster's predictions violates calibration, which requires that forecasts are unbiased conditioning on the forecasted probabilities. Two important desiderata for a calibration measure are its decision-theoretic implications (i.e., downstream decision-makers that best-respond to the forecasts are always no-regret) and its truthfulness (i.e., a forecaster approximately minimizes error by always reporting the true probabilities). Existing measures satisfy at most one of the properties, but not both.
We introduce a new calibration measure termed subsampled step calibration, $\mathsf{StepCE}^{\textsf{sub}}$, that is both decision-theoretic and truthful. In particular, on any product distribution, $\mathsf{StepCE}^{\textsf{sub}}$ is truthful up to an $O(1)$ factor whereas prior decision-theoretic calibration measures suffer from an $e^{-Ω(T)}$-$Ω(\sqrt{T})$ truthfulness gap. Moreover, in any smoothed setting where the conditional probability of each event is perturbed by a noise of magnitude $c > 0$, $\mathsf{StepCE}^{\textsf{sub}}$ is truthful up to an $O(\sqrt{\log(1/c)})$ factor, while prior decision-theoretic measures have an $e^{-Ω(T)}$-$Ω(T^{1/3})$ truthfulness gap. We also prove a general impossibility result for truthful decision-theoretic forecasting: any complete and decision-theoretic calibration measure must be discontinuous and non-truthful in the non-smoothed setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_02384 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Truthfulness of Decision-Theoretic Calibration Measures Qiao, Mingda Zhao, Eric Machine Learning Calibration measures quantify how much a forecaster's predictions violates calibration, which requires that forecasts are unbiased conditioning on the forecasted probabilities. Two important desiderata for a calibration measure are its decision-theoretic implications (i.e., downstream decision-makers that best-respond to the forecasts are always no-regret) and its truthfulness (i.e., a forecaster approximately minimizes error by always reporting the true probabilities). Existing measures satisfy at most one of the properties, but not both. We introduce a new calibration measure termed subsampled step calibration, $\mathsf{StepCE}^{\textsf{sub}}$, that is both decision-theoretic and truthful. In particular, on any product distribution, $\mathsf{StepCE}^{\textsf{sub}}$ is truthful up to an $O(1)$ factor whereas prior decision-theoretic calibration measures suffer from an $e^{-Ω(T)}$-$Ω(\sqrt{T})$ truthfulness gap. Moreover, in any smoothed setting where the conditional probability of each event is perturbed by a noise of magnitude $c > 0$, $\mathsf{StepCE}^{\textsf{sub}}$ is truthful up to an $O(\sqrt{\log(1/c)})$ factor, while prior decision-theoretic measures have an $e^{-Ω(T)}$-$Ω(T^{1/3})$ truthfulness gap. We also prove a general impossibility result for truthful decision-theoretic forecasting: any complete and decision-theoretic calibration measure must be discontinuous and non-truthful in the non-smoothed setting. |
| title | Truthfulness of Decision-Theoretic Calibration Measures |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2503.02384 |