Uncertainty quantification for expectation-calibrated predictions

2026-08-27

AI Summary

本文针对条件均值的校准点预测问题，利用共形预测开发了校准置信区间方法，提供不确定性量化，并通过模拟和保险数据集验证了方法的有效性。

Abstract

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.

Problem

• uncertainty quantification
• calibrated predictions
• conditional mean
• confidence intervals
• conformal prediction

Innovation

• calibrated confidence intervals
• conformal prediction
• isotonic regression