# Statistically Valid Variable Importance Assessment through Conditional Permutations

arXiv: https://arxiv.org/abs/2309.07593 · HTML: https://mlsanity.com/paper/2309.07593/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 49 references that are in the map.
- First posted on arXiv 14 Sep 2023.

## Builds on (most cited first, 14 of 14)

- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Explaining by Removing: A Unified Framework for Model Explanation](https://mlsanity.com/paper/2011.14878/) (2020)
- [Problems with Shapley-value-based explanations as feature importance measures](https://mlsanity.com/paper/2002.11097/) (2020)
- [Panning for Gold: Model-X Knockoffs for High-dimensional Controlled Variable Selection](https://mlsanity.com/paper/1610.02351/) (2016)
- [Unrestricted Permutation forces Extrapolation: Variable Importance Requires at least One More Model, or There Is No Free Variable Importance](https://mlsanity.com/paper/1905.03151/) (2019)
- [General Pitfalls of Model-Agnostic Interpretation Methods for Machine Learning Models](https://mlsanity.com/paper/2007.04131/) (2020)
- [Visualizing the Feature Importance for Black Box Models](https://mlsanity.com/paper/1804.06620/) (2018)
- [A general framework for inference on algorithm-agnostic variable importance](https://mlsanity.com/paper/2004.03683/) (2020)
- [Testing Conditional Independence in Supervised Learning Algorithms](https://mlsanity.com/paper/1901.09917/) (2019)
- [Fast and Powerful Conditional Randomization Testing via Distillation](https://mlsanity.com/paper/2006.03980/) (2020)
- [Aggregation of Multiple Knockoffs](https://mlsanity.com/paper/2002.09269/) (2020)
- [Lazy Estimation of Variable Importance for Large Neural Networks](https://mlsanity.com/paper/2207.09097/) (2022)
- [A Conditional Randomization Test for Sparse Logistic Regression in High-Dimension](https://mlsanity.com/paper/2205.14613/) (2022)

## Built on by (most cited first, 7 of 7)

- [Variable Importance in High-Dimensional Settings Requires Grouping](https://mlsanity.com/paper/2312.10858/) (2023)
- [Measuring Variable Importance in Heterogeneous Treatment Effects with Confidence](https://mlsanity.com/paper/2408.13002/) (2024)
- [Top-k Feature Importance Ranking](https://mlsanity.com/paper/2509.15420/) (2025)
- [Aggregate Models, Not Explanations: Improving Feature Importance Estimation](https://mlsanity.com/paper/2602.11760/) (2026)
- [Cognitive Networks and Performance Drive fMRI-Based State Classification Using DNN Models](https://mlsanity.com/paper/2409.00003/) (2024)
- [Targeted Learning for Variable Importance](https://mlsanity.com/paper/2411.02221/) (2024)
- [MixtureKit: A General Framework for Composing, Training, and Visualizing Mixture-of-Experts Models](https://mlsanity.com/paper/2512.12121/) (2025)

## Abstract (arXiv)

Variable importance assessment has become a crucial step in machine-learning applications when using complex learners, such as deep neural networks, on large-scale data. Removal-based importance assessment is currently the reference approach, particularly when statistical guarantees are sought to justify variable inclusion. It is often implemented with variable permutation schemes. On the flip side, these approaches risk misidentifying unimportant variables as important in the presence of correlations among covariates. Here we develop a systematic approach for studying Conditional Permutation Importance (CPI) that is model agnostic and computationally lean, as well as reusable benchmarks of state-of-the-art variable importance estimators. We show theoretically and empirically that textitCPI overcomes the limitations of standard permutation importance by providing accurate type-I error control. When used with a deep neural network, textitCPI consistently showed top accuracy across benchmarks. An experiment on real-world data analysis in a large-scale medical dataset showed that textitCPI provides a more parsimonious selection of statistically significant variables. Our results suggest that textitCPI can be readily used as drop-in replacement for permutation-based methods.