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Inferring variable importance is the key problem of many scientific studies,where researchers seek to learn the effect of a feature $X$ on the outcome $Y$in the presence of confounding variables $Z$. Focusing on classificationproblems, we define the expected total variation (ETV), which is an intuitiveand deterministic measure of variable importance that does not rely on anymodel context. We then introduce algorithms for statistical inference on theETV under design-based/model-X assumptions. These algorithms build on thefloodgate notion for regression problems (Zhang and Janson 2020). Thealgorithms we introduce can leverage any user-specified regression function andproduce asymptotic lower confidence bounds for the ETV. We show theeffectiveness of our algorithms with simulations and a case study in conjointanalysis on the US general election.

Total Variation Floodgate for Variable Importance Inference in Classification