LUCID: Local Understanding of Covariate Importance with Conditional Density Estimation
Abstract
Computing local-level variable importance (VI) is critical for understanding machine learning models. Local permutation-based VI metrics offer a simple yet powerful approach, measuring how much a model's output changes when perturbing its inputs. However, existing perturbation strategies often ignore feature dependence or account for it only through restricted approximations. Perturbing a feature without fully respecting this dependence can generate unrealistic counterfactuals, thereby evaluating the model in regions unsupported by the observed data distribution. We address this gap by introducing a new model-agnostic local VI metric and estimator, Local Understanding of Covariate Importance with conditional Density estimation (LUCID). LUCID perturbs features of interest using plausible values drawn from the full conditional distribution given the remaining observed features. We establish theoretical connections between LUCID and existing VI measures, and provide an estimator with convergence guarantees and uncertainty quantification. Finally, we demonstrate LUCID's stable performance and practical utility across simulated and real-world examples.
Related
- Minimax estimation of the expected conditional covariance under bounds on the covariate density
- Learning under Target Shift: Optimal Density Ratio Estimation and Importance-Weighted Regression
- SLGP: An R Package for Spatial Conditional Density Estimation
- Benchmarking Tabular Foundation Models for Conditional Density Estimation in Regression
- Finite-Rank Logistic Gaussian Processes with Exact Likelihood for Conditional Density Estimation
BibTeX
@misc{wang2026lucid,
title = {{LUCID: Local Understanding of Covariate Importance with Conditional Density Estimation}},
author = {Yixiao Wang and Srikar Katta and Jon Donnelly and Emanuele Borgonovo and Cynthia Rudin},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.35740},
eprint = {2610.35740},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.35740},
}
RIS
TY - UNPB
TI - LUCID: Local Understanding of Covariate Importance with Conditional Density Estimation
AU - Yixiao Wang
AU - Srikar Katta
AU - Jon Donnelly
AU - Emanuele Borgonovo
AU - Cynthia Rudin
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.35740
UR - https://arxiv.org/abs/2610.35740
AB - Computing local-level variable importance (VI) is critical for understanding machine learning models. Local permutation-based VI metrics offer a simple yet powerful approach, measuring how much a model's output changes when perturbing its inputs. However, existing perturbation strategies often ignore feature dependence or account for it only through restricted approximations. Perturbing a feature without fully respecting this dependence can generate unrealistic counterfactuals, thereby evaluating the model in regions unsupported by the observed data distribution. We address this gap by introducing a new model-agnostic local VI metric and estimator, Local Understanding of Covariate Importance with conditional Density estimation (LUCID). LUCID perturbs features of interest using plausible values drawn from the full conditional distribution given the remaining observed features. We establish theoretical connections between LUCID and existing VI measures, and provide an estimator with convergence guarantees and uncertainty quantification. Finally, we demonstrate LUCID's stable performance and practical utility across simulated and real-world examples.
ER -