Abstract: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.
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2605.01066 [cs.LG] |
| (or arXiv:2605.01066v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2605.01066 arXiv-issued DOI via DataCite (pending registration) |
From: Jaesung Yoo [view email]
[v1]
Fri, 1 May 2026 20:00:36 UTC (21,071 KB)
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