Reproduce “Scaling-Score Conformal Prediction for Multi-Target Regression” on OpenResearch

About this paper

Sylvain Rousseau, Soundouss Messoudi

Scaling-Score Conformal Prediction constructs joint prediction regions for multi-target regression by normalizing component-wise residuals with transductive, quantile-based scales. It retains finite-sample, model-agnostic coverage under exchangeability while adapting to heterogeneous target errors; across 29 datasets, its staircase approximation generally reduced region volume relative to standard maximum-residual hypercubes, although zero-residual quantiles can cause coverage failures in some settings.

Key insights

• A shared conformal inflation factor can be combined with target-specific residual scales without requiring a distributional model or a second calibration split.
• The exact region is downward-closed and decomposes into 3^d cells; although the staircase has exponential worst-case complexity, Pareto pruning leaves very few active rectangles at higher dimensions.
• The default choice gamma = 1 - alpha is generally reliable, but zero or near-zero residual order statistics can invalidate region assumptions and require special treatment.

Summary by alphaXiv.