In a sequential regression setting, a decision-maker may be primarily concerned with whether the future observation will increase or decrease compared to the current one, rather than the actual value of the future observation. In this context, we introduce the notion of parity calibration, which captures the goal of calibrated forecasting for the increase-decrease (or "parity") event in a timeseries. Parity probabilities can be extracted from a forecasted distribution for the output, but we show that such a strategy leads to theoretical unpredictability and poor practical performance. We then observe that although the original task was regression, parity calibration can be expressed as binary calibration. Drawing on this connection, we use an online binary calibration method to achieve parity calibration. We demonstrate the effectiveness of our approach on real-world case studies in epidemiology, weather forecasting, and model-based control in nuclear fusion.

翻译：在序贯回归问题中，决策者可能更关心未来观测值相较于当前值会上升还是下降，而非未来观测值的具体数值。针对这一场景，我们引入"奇偶校准"概念，该概念旨在实现对时间序列中"上升-下降"（即"奇偶"）事件的校准预测。虽然奇偶概率可从输出值的预测分布中提取，但研究表明此类策略会导致理论不可预测性及实际性能低下。我们进一步发现，尽管原始任务属于回归问题，但奇偶校准可转化为二元校准问题。基于这一联系，我们采用在线二元校准方法实现奇偶校准。通过流行病学、天气预报及核聚变模型控制等真实案例研究，我们验证了该方法的有效性。