期望校准预测的不确定性量化
Uncertainty quantification for expectation-calibrated predictions
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中文总结 AI 辅助
该研究针对条件均值的校准点预测问题，借助共形预测构建了两种分箱方案的校准置信区间，经模拟与保险数据集验证，其具备无分布理论保证与良好经验性能。
中文摘要 AI 辅助
现有模型校准的文献主要聚焦于分类与概率预测。在本研究中，我们针对条件均值的校准点预测展开探讨。尽管现有不可能性结果排除了 exact 样本外校准预测的可能性，但我们构建了围绕此类预测提供不确定性量化的校准置信区间。我们的结果具备无分布理论保证，适用于模型无关、有限样本且满足可交换性的场景，这得益于共形预测（conformal prediction）的应用。校准置信区间依赖于通用的底层分箱方案，我们给出两种分箱方案示例：一种基于与数据无关的划分，另一种基于保序回归（isotonic regression）。在结构假设下，我们证明基于保序回归的校准置信区间具备强渐近一致性性质，且其宽度渐近趋于零。我们通过在模拟场景及高度不平衡的保险数据集上应用所提方法，验证了其经验性能。
英文摘要
The existing literature on model calibration focuses mainly on classification and probabilistic prediction. In this work, we address calibrated point predictions for the conditional mean. Although existing impossibility results preclude exact out-of-sample calibrated predictions, we develop calibrated confidence intervals that provide uncertainty quantification around such predictions. Our results come with distribution-free theoretical guarantees and are applicable in model-agnostic, finite-sample settings under exchangeability by leveraging conformal prediction. Calibrated confidence intervals rely on a general underlying binning scheme. We present two examples of such a binning scheme, one based on a data-independent partition and the other on isotonic regression. Under structural assumptions, we prove that calibrated confidence intervals based on isotonic regression come with strong asymptotic consistency properties and have an asymptotically vanishing width. We illustrate the empirical performance of our methods by applying them first in a simulated setting and then to a highly imbalanced insurance dataset.
