CLAPS: Aleatoric-Epistemic Scaling via Last-Layer Laplace for Conformal Regression

TL;DR

CLAPS introduces a novel conformal regression method that adaptively scales prediction intervals by combining aleatoric and epistemic uncertainties using last-layer Laplace approximation, ensuring valid, efficient coverage.

Contribution

It proposes a new heteroscedastic last-layer Laplace-based scaling method for conformal regression that explicitly accounts for both aleatoric and epistemic uncertainties.

Findings

Achieves nominal-level coverage in experiments.

Provides competitive interval efficiency.

Reduces to aleatoric scaling as epistemic uncertainty contracts.

Abstract

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.