A dimensional R2 regression metric
For practitioners evaluating regression models, Dim-R2 addresses key limitations of R2 but is an incremental improvement.
The paper introduces Dim-R2, an extension of the R2 score that handles arbitrary dimensionality, provides multidimensional accuracy views, and reduces noise sensitivity. It demonstrates advantages on synthetic and three real datasets.
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.