Scaling-score method improves reliable multi-output predictions jointly
Scaling-Score Conformal Prediction for Multi-Target Regression
Artificial Intelligence
Summary
Many problems need predictions for several connected things at once, like predicting weather measures together. Making sure all those predictions are reliably accurate as a group is tough. The authors created a new approach called scaling-score conformal prediction, which works with any basic prediction model and uses existing data more efficiently. Their method produces different kinds of prediction regions that balance coverage accuracy and size, with one simple setting controlling this balance. Tests on many datasets showed their approach maintains reliable joint accuracy and often makes smaller prediction regions than other methods.
What this means in practice
- •For data science teams: Create prediction intervals that reliably cover all related outputs together without needing special model training.
- •For industrial process engineers: Provide trustworthy multi-output forecasts with controlled uncertainty for complex manufacturing parameters simultaneously.
Authors
Sylvain Rousseau, Soundouss Messoudi
Abstract
Multi-target regression requires a model to simultaneously predict several related outputs. Conformal prediction provides distribution-free, finite-sample marginal coverage guarantees, but extending these to joint multi-dimensional regions in a model-agnostic, sample-efficient manner remains challenging: max-aggregation ignores scale differences, copula-based methods are only asymptotically valid, rectangular methods typically split the calibration set, and quantile or density-based methods require training a specialised model beyond a plain point predictor. We propose the scaling-score conformal method, which is model-agnostic (requires only component-wise absolute residuals), uses a single calibration set, and yields four nested output types: an outer rectangle (SCO) with valid joint coverage, the exact set R $α$ , a staircase (SC 2 ) over approximation of R $α$ , and an inner rectangle (SCI). A single hyperparameter $γ$ $\in$ (0, 1) controls the base-rectangle quantile level independently of $α$. We prove downward-closedness and a rectangular sandwich bound and derive a closed-form outer rectangle. Experiments on 29 realworld datasets confirm valid joint coverage; SC 2 with $γ$ = 1-$α$ consistently achieves competitive volume relative to baselines, with the advantage growing with output dimension d.