CLAPS: Posterior-Aware Conformal Intervals via Last-Layer Laplace

arXiv:2512.01384v3 Announce Type: replace-cross
Abstract: 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.