A dimensional R2 regression metric

TL;DR

The paper introduces Dimensional R2 (Dim-R2), an extension of the R2 score for evaluating regression models on high-dimensional data, providing more interpretability and robustness.

Contribution

It proposes Dim-R2, a novel regression metric that handles arbitrary dimensions, offers a multidimensional accuracy view, and reduces noise sensitivity.

Findings

Dim-R2 effectively evaluates high-dimensional regression data.

Dim-R2 reveals detailed accuracy patterns not visible with traditional R2.

Dim-R2 demonstrates advantages on synthetic and real datasets.

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.