We present CLAPS, a posterior-aware conformal regression method that pairs a Last-Layer Laplace Approximation with split-conformal calibration. From the resulting Gaussian posterior, CLAPS defines a simple two-sided posterior CDF score that aligns the conformity metric with the full predictive shape, not just a point estimate. This alignment can yield substantially narrower prediction intervals at a fixed target coverage, particularly on small to medium tabular datasets where data are scarce and uncertainty modeling is informative. We also provide a lightweight diagnostic suite that separates aleatoric and epistemic components and visualizes posterior behavior, helping practitioners assess when and why intervals shrink. Across multiple benchmarks using the same MLP backbone, CLAPS achieves nominal coverage and offers the most efficient intervals on small to medium datasets with mild heterogeneity, while remaining competitive and diagnostically transparent on large-scale heterogeneous data where Normalized-CP and CQR attain the tightest intervals.

翻译：我们提出CLAPS，一种后验感知的共形回归方法，它将最后一层拉普拉斯近似与分割共形校准相结合。基于所得的高斯后验，CLAPS定义了一个简单的双侧后验CDF评分函数，使一致性度量与完整的预测分布形状对齐，而不仅仅是点估计。这种对齐可以在固定的目标覆盖水平下产生显著更窄的预测区间，特别是在数据稀缺且不确定性建模具有信息价值的中小型表格数据集上。我们还提供了一套轻量级诊断工具，用于分离偶然不确定性和认知不确定性成分，并可视化后验行为，帮助实践者评估区间何时以及为何收缩。在使用相同MLP骨干网络的多个基准测试中，CLAPS在轻度异质性的中小型数据集上实现了名义覆盖水平，并提供了最高效的区间；而在大规模异质数据上，尽管Normalized-CP和CQR获得了最紧凑的区间，CLAPS仍保持竞争力并具备诊断透明性。