多目标回归的缩放分数共形预测
Scaling-Score Conformal Prediction for Multi-Target Regression
- CNRS（法国国家科学研究中心）
- Heudiasyc（Heudiasyc实验室）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
针对多目标回归的联合共形预测难题，提出模型无关的缩放分数共形方法，仅需绝对残差和单一校准集，提供四种嵌套输出区域，并在29个数据集上验证了有效覆盖与体积优势。
AI中文摘要：
多目标回归要求模型同时预测多个相关输出。共形预测提供了无分布假设、有限样本的边际覆盖保证，但以模型无关且样本高效的方式将其扩展到联合多维区域仍然具有挑战性：最大聚合忽略了尺度差异，基于copula的方法仅具有渐近有效性，矩形方法通常需要分割校准集，而分位数或基于密度的方法需要训练一个超越普通点预测器的专门模型。我们提出了缩放分数共形方法，它是模型无关的（仅需要分量方向的绝对残差），使用单一校准集，并产生四种嵌套的输出类型：具有有效联合覆盖的外矩形（SCO）、精确集合R α、R α的阶梯（SC 2）过度近似，以及内矩形（SCI）。单个超参数γ ∈ (0, 1)独立于α控制基础矩形的分位数水平。我们证明了向下封闭性和矩形夹心界，并推导出封闭形式的外矩形。在29个真实世界数据集上的实验证实了有效的联合覆盖；γ = 1-α的SC 2在体积上持续达到与基线相当的水平，且优势随输出维度d的增加而增长。
英文摘要：
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.
