Sobol-CPI: a Doubly Robust Conditional Permutation Importance Statistic
Published in Preprint, 2025
In this work, we first aim to provide a theoretical framework for Conditional Permutation Importance (CPI) by proving and specifying the assumptions under which the conditional distribution step is valid. CPI involves the estimation of the Total Sobol Index, which is typically estimated with removal-based approaches such as Leave One Covariate Out (LOCO). Here, we introduce \textit{Robust-CPI}, a variation of CPI that enables We then formalize the advantages of this permutation-based approach over LOCO, as Robust-CPI benefits from an implicit bias that induces double robustness in detecting the null hypothesis, while LOCO suffers a double optimization error that limits its effectiveness. Finally, we validate our findings through numerical experiments.
Recommended citation: Reyero Lobo, A., Neuvial, P., and Thirion, B. Sobol-cpi: a doubly robust conditional permutation importance statistic. 2025
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