让多个分位数预测同时校准，且不降低原模型性能。
Calibrated Multi-Level Quantile Forecasting
- 通过轻量级追踪器动态调整分位数预测，保证多层级校准。
- 在真实疫情与能源预测中显著提升校准度，损失几乎不变。
- 适合对预测可靠性要求高的场景，如医疗、能源调度。
我们提出一种在线方法，可同时保证多个分位数水平的预测校准。若某分位数α的预测值在α比例的时间点上大于等于目标值，则称该序列校准。本文方法称为多层级分位数追踪器（MultiQT），可嵌入任意点预测或分位数预测模型，生成保证校准的分位数预测，即使面对对抗性分布偏移也有效。关键优势在于保持分位数有序性（如0.5分位数不大于0.6分位数），并具有无悔保证，即渐近不会损害原模型在分位数损失上的表现。实验表明，MultiQT在流行病与能源预测任务中显著改善校准性，而分位数损失基本不变或略有提升。
原文摘要 · Abstract (English)
We develop an online method that guarantees calibration of quantile forecasts at multiple quantile levels simultaneously. In this work, a sequence of quantile forecasts is said to be calibrated provided that its $α$-level predictions are greater than or equal to the target value at an $α$ fraction of time steps, for each level $α$. Our procedure, called the multi-level quantile tracker (MultiQT), is lightweight and wraps around any point or quantile forecaster to produce adjusted quantile forecasts that are guaranteed to be calibrated, even against adversarial distribution shifts. Critically, it does so while ensuring that the quantiles remain ordered, e.g., the 0.5-level quantile forecast will never be larger than the 0.6-level forecast. Moreover, the method has a no-regret guarantee, implying it will not degrade the performance of the existing forecaster (asymptotically), with respect to the quantile loss. In our experiments, we find that MultiQT significantly improves the calibration of real forecasters in epidemic and energy forecasting problems, while leaving the quantile loss largely unchanged or slightly improved.
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