发表机构
University of Southern California; ETH Zürich（南加州大学; 苏黎世联邦理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对随机离散采样的连续时间轨迹不确定性量化难题，提出利用轨迹正则性属性、结合高频校准数据估计边界的共形预测算法，经实验验证可实现全轨迹有效覆盖率。
AI 中文摘要
连续时间轨迹的不确定性量化是众多安全关键工程领域的前提条件。然而，数据驱动不确定性量化面临的一大挑战是，校准轨迹仅以离散、通常稀疏且随机的时间间隔采样。标准共形预测方法通常无法在采样时间之间提供保证。在本研究中，我们引入一种新技术，以获取在离散且可能随机时间采样的连续时间轨迹的有效共形预测区域。为实现这一目标，我们做出三项贡献：（1）提供一种算法，利用基础轨迹的正则性属性来获取采样点之间的有效预测区域；（2）提供从额外高频校准数据集估计上述正则性属性有效边界的方法；（3）引入并比较多种处理随机采样时间的算法。最后，我们通过实验验证，我们的方法在整个连续轨迹上实现了有效覆盖率。
英文摘要
Uncertainty quantification for continuous-time trajectories is a prerequisite in many safety-critical engineering domains. However, a major challenge in data-driven uncertainty quantification is that calibration trajectories are sampled only at discrete, often sparse, and random intervals. Standard conformal prediction methods typically fail to provide guarantees in between sampling times. In this work, we introduce a new technique to obtain valid conformal prediction regions for continuous-time trajectories that are sampled at discrete and possibly random times. To accomplish this goal, we make three contributions: (1) we provide an algorithm that leverages regularity properties of the underlying trajectories to obtain valid prediction regions in between samples, (2) we provide methods that estimate valid bounds on the aforementioned regularity properties from an additional high-frequency calibration dataset, and (3) we introduce and compare several algorithms to deal with random sampling times. Finally, we present experiments where we validate that our methods achieve valid coverage across the entire continuous trajectory.
