Understanding model predictions when inputs are correlated

Functional ANOVA decomposes predictions into interpretable main effects and interactions, but existing methods assume independent inputs—unrealistic for real data. This work extends functional ANOVA to dependent continuous inputs using Hilbert space theory, deriving an explicit Riesz basis representation that recovers the classical independent case as a special case. The authors propose a model-agnostic algorithm to estimate this decomposition from finite samples and compare it empirically against SHAP and other explanation methods, showing improved interpretability across tested scenarios.