发表机构
Stanford University（斯坦福大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究分析延迟反馈下自适应共形推断的覆盖保证，提出延迟-记忆比诊断，揭示延迟影响取决于残差过程的时间尺度。
AI 中文摘要
自适应共形推断（ACI）通过在线调整名义误覆盖水平以响应最近的覆盖误差，将共形预测扩展到非可交换环境。然而，当预测以水平τ发布时，评估预测所需的结果仅在τ步之后才能观察到，因此这些自适应更新必须依赖延迟反馈。我们研究这一设置，并探讨延迟的影响如何取决于残差过程的持续性。首先，我们证明τ延迟的ACI递归可以分解为τ个交错ACI类序列。这种表示产生了长期经验覆盖的有限样本界，并显式依赖于τ。我们还推导了一个近似边际覆盖界，该界将覆盖偏差与预测范围内底层环境的变化以及适应率γ联系起来。接着，我们引入延迟-记忆比r=τ/L，其中L是驱动非交换性的时间信号衰减的时间尺度。模拟结果表明，该比率的实用性取决于时间依赖的形式：它在AR(1)依赖下强烈组织性能，在GARCH(1,1)和马尔可夫切换下对整体性能的预测性较弱，但在这些设置中更清晰地刻画了尺度归一化何时仍然有用。突变均值和方差偏移实验进一步表明，优选的适应率取决于残差动态。总体而言，结果表明预测延迟的影响最好相对于过去残差信息保持相关的时间尺度来理解。
英文摘要
Adaptive Conformal Inference (ACI) extends conformal prediction to non-exchangeable settings by adjusting the nominal miscoverage level online in response to recent coverage errors. When forecasts are issued with horizon $τ$, however, the outcome needed to evaluate a prediction is observed only $τ$ steps later, so these adaptive updates must rely on delayed feedback. We study this setting and ask how the effect of delay depends on the persistence of the residual process. First, we show that the $τ$-delayed ACI recursion can be decomposed into $τ$ interleaved ACI-like sequences. This representation yields a finite-sample bound on long-run empirical coverage with explicit dependence on $τ$. We also derive an approximate marginal coverage bound that relates coverage deviation to changes in the underlying environment across the forecast horizon and to the adaptation rate $γ$. We then introduce the delay-to-memory ratio $r=τ/L$, where $L$ is the time scale over which the temporal signal driving non-exchangeability decays. Simulation results show that the usefulness of this ratio depends on the form of temporal dependence: it strongly organizes performance under AR(1) dependence, is less predictive of overall performance under GARCH(1,1) and Markov switching, but more clearly characterizes when scale normalization remains useful in those settings. Abrupt mean- and variance-shift experiments further show that the preferred adaptation rate depends on the residual dynamics. Overall, the results show that the effect of forecast delay is best understood relative to the time scale over which past residual information remains relevant.
