# Total Variation Floodgate for Variable Importance Inference in Classification

arXiv: https://arxiv.org/abs/2309.04002 · HTML: https://mlsanity.com/paper/2309.04002/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Sep 2023.

## Built on by (most cited first, 1 of 1)

- [Statistical Inference and Learning for Shapley Additive Explanations (SHAP)](https://mlsanity.com/paper/2602.10532/) (2026)

## Abstract (arXiv)

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 classification problems, we define the expected total variation (ETV), which is an intuitive and deterministic measure of variable importance that does not rely on any model context. We then introduce algorithms for statistical inference on the ETV under design-based/model-X assumptions. These algorithms build on the floodgate notion for regression problems (Zhang and Janson 2020). The algorithms we introduce can leverage any user-specified regression function and produce asymptotic lower confidence bounds for the ETV. We show the effectiveness of our algorithms with simulations and a case study in conjoint analysis on the US general election.