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.

翻译：本文提出一种在线方法，可同时保证多个分位数水平预测的校准性。在本研究中，当每个水平α的α水平预测在时间步长的α比例上大于或等于目标值时，该分位数预测序列即被称为已校准。我们提出的方法称为多水平分位数追踪器（MultiQT），该方法具有轻量级特性，可封装任意点预测或分位数预测器，生成经调整且保证校准的分位数预测——即使面对对抗性分布偏移时亦然。关键在于，该方法在确保分位数保持有序性的同时实现校准，例如0.5水平分位数预测永远不会大于0.6水平预测。此外，该方法具有无遗憾保证，意味着在分位数损失方面不会（渐近地）降低现有预测器的性能。实验表明，在流行病预测和能源预测问题中，MultiQT能显著提升实际预测器的校准性，同时使分位数损失基本保持不变或略有改善。