Scaling-Score Conformal Prediction for Multi-Target Regression

arXiv:2609.17091v1 Announce Type: new 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 $\alpha$ , a staircase (SC 2 ) over approximation of R $\alpha$ , and an inner rectangle (SCI). A single hyperparameter $\gamma$ $\in$ (0, 1) controls the base-rectangle quantile level independently of $\alpha$. 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 $\gamma$ = 1-$\alpha$ consistently achieves competitive volume relative to baselines, with the advantage growing with output dimension d.

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 $\alpha$ , a staircase (SC 2 ) over approximation of R $\alpha$ , and an inner rectangle (SCI). A single hyperparameter $\gamma$ $\in$ (0, 1) controls the base-rectangle quantile level independently of $\alpha$. 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 $\gamma$ = 1-$\alpha$ consistently achieves competitive volume relative to baselines, with the advantage growing with output dimension d.

Artificial Intelligence (cs.AI)

arXiv:2609.17091 [cs.AI]

(or arXiv:2609.17091v1 [cs.AI] for this version)

https://doi.org/10.48550/arXiv.2609.17091 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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Scaling-Score Conformal Prediction for Multi-Target Regression

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