Marques & Graziadei's skew-adaptive method tightens prediction intervals

Conformal prediction guarantees valid prediction intervals for any regression model, but standard methods assume symmetric errors—a poor fit for real-world data with heteroskedasticity and skewness. In this paper, Marques and Graziadei propose a skew-adaptive extension of split conformal prediction. They start from an asymmetric interval family centered on a point prediction, then derive a conformity score using a gauge approach. The key innovation is using the inverse hyperbolic sine transform of signed scaled residuals as a training target for an additional model, which learns how predictive uncertainty should tilt (i.e., skew) across the feature space. This preserves the finite-sample marginal validity of split conformal prediction under exchangeability while producing intervals that adapt to both local scale and local skewness.

The authors also develop a calibration-sample-based estimator for comparing expected relative width of skew-adaptive versus classical scaled-score intervals. Experiments across multiple datasets demonstrate consistent gains in prediction interval efficiency over both the scaled-score construction and conformalized quantile regression (CQR). The proposed estimator closely matches the average width ratio observed on test samples, validating the approach. This work offers a principled way to produce tighter, more informative uncertainty intervals for regression models, particularly useful in applications where error distributions vary systematically with input features.