Distribution-free prediction sets play a pivotal role in uncertainty quantification for complex statistical models. Their validity hinges on reliable calibration data, which may not be readily available as real-world environments often undergo unknown changes over time. In this paper, we propose a strategy for choosing an adaptive window and use the data therein to construct prediction sets. The window is selected by optimizing an estimated bias-variance tradeoff. We provide sharp coverage guarantees for our method, showing its adaptivity to the underlying temporal drift. We also illustrate its efficacy through numerical experiments on synthetic and real data.

翻译：无分布预测集在复杂统计模型的不确定性量化中扮演着关键角色。其有效性依赖于可靠的校准数据，然而现实环境常随时间发生未知变化，导致此类数据难以获取。本文提出一种自适应窗口选择策略，并利用窗口内数据构建预测集。该窗口通过优化估计的偏差-方差权衡进行选取。我们为所提方法提供了严格的覆盖保证，证明其对潜在时间漂移具有自适应性。通过合成数据与真实数据的数值实验，进一步验证了该方法的有效性。