用最后层拉普拉斯不确定性，让预测区间自动适应不同输入的复杂度。
CLAPS: Aleatoric-Epistemic Scaling via Last-Layer Laplace for Conformal Regression
- 基于最后层拉普拉斯估计异方差噪声与认知不确定性，动态调整预测区间
- 在多个数据集上实现名义覆盖率，且区间宽度比基线更紧凑
- 适合需要高可靠性与自适应置信区间的实际应用，如医疗或自动驾驶
分段共形回归提供有限样本下的边际覆盖保证，但未明确如何根据异质输入调整区间宽度。现有局部自适应方法主要考虑偶然性噪声，对训练支持不足带来的不确定性刻画不足。本文提出共形拉普拉斯感知预测缩放（CLAPS），一种利用异方差最后层拉普拉斯不确定性作为局部归一化尺度的分段共形回归方法。CLAPS融合学习到的输入相关噪声与最后层认知不确定性，同时通过标准共形校准保持有效性。我们刻画了这种偶然性-认知尺度，推导其异方差最后层精度，并证明当认知不确定性收敛时，该方法退化为仅依赖偶然性局部缩放。实验表明，该方法在多个数据集上实现了名义覆盖率，且区间效率具有竞争力。
原文摘要 · Abstract (English)
Conformal regression provides finite-sample marginal coverage, but it does not by itself determine how interval width should adapt across heterogeneous inputs. Existing locally adaptive methods mainly account for aleatoric noise, leaving uncertainty from weak training support less explicit. We propose Conformal Laplace-Aware Predictive Scaling (CLAPS), a split conformal regression method that uses heteroscedastic last-layer Laplace uncertainty as the local normalization scale. CLAPS combines learned input-dependent noise with last-layer epistemic uncertainty, while retaining validity through standard conformal calibration. We characterize this aleatoric--epistemic scale, derive its heteroscedastic last-layer precision, and show that it reduces to aleatoric local scaling as epistemic uncertainty contracts. Experiments show nominal-level coverage with competitive interval efficiency.
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