# Disentangled Feature Importance

arXiv: https://arxiv.org/abs/2507.00260 · HTML: https://mlsanity.com/paper/2507.00260/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Jun 2025.

## Built on by (most cited first, 2 of 2)

- [LOCO-AdaMP: Built-in LOCO Inference for Adaptive Minipatch Ensembles with Enhanced Prediction](https://mlsanity.com/paper/2609.36396/) (2026)
- [What Do Sparse Autoencoder Feature Discovery Scores Identify? From Activations to Interventions](https://mlsanity.com/paper/2610.15850/) (2026)

## Abstract (arXiv)

When predictors are statistically dependent, the appropriate definition of feature importance depends on the operational goal. Conditional-incremental measures are well-suited for feature selection, acquisition, and compression, where shared predictive information is treated as redundancy. For post-hoc interpretation, however, the goal is often to attribute predictive signals across correlated measurement channels. We introduce Disentangled Feature Importance (DFI), a population-level attribution framework for this setting. DFI maps covariates to an independent latent representation under a specified entropic optimal transport geometry, computes latent importance, and attributes it back to the original covariates through barycentric sensitivities. We show that broad conditional-incremental FI functionals target conditional incremental predictive value under squared-error loss, and therefore answer a different question from attribution of shared predictive signal under dependence. Under fixed transport cost, reference law, and regularization level, DFI defines a well-specified family of estimands. Latent scores admit a functional ANOVA interpretation, and in the Gaussian linear case, the attributed DFI recovers the classical R2 decomposition for correlated regressors. We derive influence-function-based inference under nuisance-rate and smoothness conditions, and show in simulations and an HIV-1 neutralization-resistance analysis that DFI yields stable, interpretable, uncertainty-quantified attributions of shared predictive signal.