Scaling-Score Conformal Prediction for Multi-Target Regression

2026-09-15

AI Summary

本文提出了一种解决多目标回归中联合覆盖问题的新方法——缩放分数保形预测，该方法模型无关且仅需单一校准集。

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.

Problem

• multi-target regression
• conformal prediction
• joint coverage
• model-agnostic
• sample-efficient

Innovation

• scaling-score conformal prediction
• multi-target regression
• model-agnostic
• single calibration set
• nested output types