提出多维R2度量，解决传统R2维度受限、易受噪声干扰问题。
A dimensional R2 regression metric
- 扩展R2至任意维度输入，支持多维误差分析。
- 在合成数据和三个真实数据集上表现更稳定，避免负值异常。
- 适合需要细粒度评估回归模型性能的研究者使用。
R2评分是回归任务的标准评价指标，提供一种归一化的、与量级无关的准确性度量，能反映方差变化。然而，R2存在三个关键局限：最多仅支持二维输入；将结果简化为单一标量，掩盖了预测精度的丰富模式；对低方差噪声通道敏感，可能导致大且不可解释的负值。本文提出维度化R2评分（Dim-R2），是对R2的简单扩展，可处理任意维度数据，提供多维精度视图，并降低对噪声的敏感性。我们在合成正弦数据及三个多维回归数据集上验证了其优势。Dim-R2是一种可解释性强、灵活的度量，能揭示回归精度中的模式，指导建模过程。
原文摘要 · Abstract (English)
R2 score is the standard metric for evaluating regression tasks, offering a normalized magnitude-agnostic measure of accuracy that captures variance. However, R2 has three key limitations: it is limited to at most two dimensional inputs, it reduces the score to a single scalar that hides rich patterns of prediction accuracy, and it is sensitive to low-variance noise channels which can yield large, uninterpretable negative values. We introduce the Dimensional R2 score (Dim-R2), a simple extension of R2 that accepts data of arbitrary dimensionality, provides a multidimensional view of accuracy, and reduces sensitivity to noise. We demonstrate its advantages on both synthetic sinusoidal data and three multidimensional regression datasets. Dim-R2 offers an interpretable and flexible metric that highlights patterns in regression accuracy, guiding regression modeling.
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