Statistically Valid Variable Importance Assessment through Conditional Permutations

TL;DR

This paper introduces Conditional Permutation Importance (CPI), a statistically valid, model-agnostic method for variable importance assessment that effectively handles correlated variables and outperforms standard permutation methods in accuracy and reliability.

Contribution

The paper develops CPI, a new importance measure that overcomes limitations of existing permutation methods, with theoretical guarantees and practical effectiveness demonstrated on neural networks and real data.

Findings

CPI provides accurate type-I error control.

CPI outperforms standard permutation importance in benchmarks.

CPI yields more parsimonious variable selection in real-world data.

Abstract

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 $\textit{CPI}$ overcomes the limitations of standard permutation importance by providing accurate type-I error control. When used with a deep neural network, $\textit{CPI}$ consistently showed top accuracy across benchmarks. An experiment on real-world data analysis in a large-scale medical dataset showed that $\textit{CPI}$ provides a more parsimonious selection of statistically significant variables. Our results suggest that $\textit{CPI}$ can be readily used as drop-in replacement for permutation-based methods.