HKU IDS Scholar

Feature importance quantification faces a fundamental challenge: when predictors are correlated, standard methods systematically underestimate their contributions. We prove that major existing approaches target identical population functionals under squared-error loss, revealing why they share this correlation-induced bias. To address this limitation, we introduce Disentangled Feature Importance (DFI), a nonparametric generalization of the classical R-squared decomposition via optimal transport. DFI transforms correlated features into independent latent variables using a transport map, eliminating correlation distortion. Importance is computed in this disentangled space and attributed back through the transport map’s sensitivity. DFI provides a principled decomposition of importance scores that sum to the total predictive variability for latent additive models and to interaction-weighted functional ANOVA variances more generally, under arbitrary feature dependencies.
We develop a comprehensive semiparametric theory for DFI. For general transport maps, we establish root-n consistency and asymptotic normality of importance estimators in the latent space, which extends to the original feature space for the Bures-Wasserstein map. Notably, our estimators achieve second-order estimation error. By design, DFI avoids the computational burden of repeated submodel refitting and the challenges of conditional covariate distribution estimation, thereby achieving computational efficiency.