Multi‑target regression requires a model to predict several related outputs simultaneously. Conformal prediction offers distribution‑free finite‑sample marginal coverage guarantees, yet extending these guarantees to joint multi‑dimensional regions in a model‑agnostic and sample‑efficient way remains difficult. Existing approaches suffer from various drawbacks: max‑aggregation ignores scale differences, copula‑based methods are only asymptotically valid, rectangular methods usually split the calibration set, and quantile or density‑based methods need a specialized model beyond a plain point predictor. We propose the scaling‑score conformal method, which only needs component‑wise absolute residuals, stays model‑agnostic, 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 approximation (SC2) 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, a rectangular sandwich bound, and derive a closed‑form outer rectangle. Experiments on 29 real‑world datasets confirm valid joint coverage; with $\gamma = 1-\alpha$, SC2 consistently achieves competitive volume relative to baselines, and the advantage grows with output dimension $d$.
Review: The approach balances simplicity and rigorous uncertainty quantification for high‑dimensional multi‑target regression, making it highly applicable in practice.