用对称性信息让预测不确定性更小，高置信度下效果更明显。
eCP: Equivariant Conformal Prediction with pre-trained models
- 通过预训练模型的群平均，将非符合度分布到对称轨道上
- 理论证明非符合度得分在凸序下收缩，置信区间更紧
- 适合需要高置信度不确定量化场景，如行人轨迹预测
共形预测是一种后处理、无需分布假设、有限样本下具有形式覆盖保证的不确定性量化方法，但其在长时任务中不确定性区域可能急剧扩大，导致统计保证失去意义。为此，我们提出通过群平均预训练预测器，将非符合度质量分布在对称轨道上。每个样本被视为轨道的代表，可通过对称元素关联的其他样本减轻其不确定性。该方法在凸序下严格收缩非符合度得分，意味着改进的指数尾部界和期望上更紧的共形预测集，尤其在高置信水平下表现更优。我们进一步设计实验验证这些理论结论在行人轨迹预测中的有效性。
原文摘要 · Abstract (English)
Conformal prediction, a post-hoc, distribution-free, finite-sample method of uncertainty quantification that offers formal coverage guarantees under the assumption of data exchangeability. Unfortunately, the resulting uncertainty regions can grow significantly in long horizon missions, rendering the statistical guarantees uninformative. To that end, we propose infusing CP with geometric information via group-averaging of the pretrained predictor to distribute the non-conformity mass across the orbits. Each sample now is treated as a representative of an orbit, thus uncertainty can be mitigated by other samples entangled to it via the orbit inducing elements of the symmetry group. Our approach provably yields contracted non-conformity scores in increasing convex order, implying improved exponential-tail bounds and sharper conformal prediction sets in expectation, especially at high confidence levels. We then propose an experimental design to test these theoretical claims in pedestrian trajectory prediction.
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