Regional Explanations: Bridging Local and Global Variable Importance

We analyze two widely used local attribution methods, Local Shapley Values and LIME, which aim to quantify the contribution of a feature value xi to a specific prediction f(x1,...,xp). Despite their widespread use, we identify fundamental limitations in their ability to reliably detect locally important features, even under ideal conditions with exact computations and independent features. We argue that a sound local attribution method should not assign importance to features that neither influence the model output (e.g., features with zero coefficients in a linear model) nor exhibit statistical dependence with functionality-relevant features. We demonstrate that both Local SV and LIME violate this fundamental principle. To address this, we propose R-LOCO (Regional Leave Out COvariates), which bridges the gap between local and global explanations and provides more accurate attributions.