# Model free variable importance for high dimensional data

arXiv: https://arxiv.org/abs/2211.08414 · HTML: https://mlsanity.com/paper/2211.08414/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 49 references that are in the map.
- First posted on arXiv 15 Nov 2022.

## Builds on (most cited first, 17 of 17)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [RISE: Randomized Input Sampling for Explanation of Black-box Models](https://mlsanity.com/paper/1806.07421/) (2018)
- [A Benchmark for Interpretability Methods in Deep Neural Networks](https://mlsanity.com/paper/1806.10758/) (2018)
- [The many Shapley values for model explanation](https://mlsanity.com/paper/1908.08474/) (2019)
- [Explaining individual predictions when features are dependent: More accurate approximations to Shapley values](https://mlsanity.com/paper/1903.10464/) (2019)
- [Problems with Shapley-value-based explanations as feature importance measures](https://mlsanity.com/paper/2002.11097/) (2020)
- [Leveraging Explanations in Interactive Machine Learning: An Overview](https://mlsanity.com/paper/2207.14526/) (2022)
- [A simple measure of conditional dependence](https://mlsanity.com/paper/1910.12327/) (2019)
- [Explaining a Series of Models by Propagating Shapley Values](https://mlsanity.com/paper/2105.00108/) (2021)
- [Explaining black box decisions by Shapley cohort refinement](https://mlsanity.com/paper/1911.00467/) (2019)
- [Floodgate: inference for model-free variable importance](https://mlsanity.com/paper/2007.01283/) (2020)
- [Deletion and Insertion Tests in Regression Models](https://mlsanity.com/paper/2205.12423/) (2022)
- [Cohort Shapley value for algorithmic fairness](https://mlsanity.com/paper/2105.07168/) (2021)
- [Variable importance without impossible data](https://mlsanity.com/paper/2205.15750/) (2022)
- [Proportional marginal effects for global sensitivity analysis](https://mlsanity.com/paper/2210.13065/) (2022)

## Built on by (most cited first, 3 of 3)

- [Factor Importance Ranking and Selection using Total Indices](https://mlsanity.com/paper/2401.00800/) (2024)
- [Uncertainty Quantification for Local Model Explanations Without Model Access](https://mlsanity.com/paper/2301.05761/) (2023)
- [AICO: Feature Significance Tests for Supervised Learning](https://mlsanity.com/paper/2506.23396/) (2025)

## Abstract (arXiv)

A model-agnostic variable importance method can be used with arbitrary prediction functions. Here we present some model-free methods that do not require access to the prediction function. This is useful when that function is proprietary and not available, or just extremely expensive. It is also useful when studying residuals from a model. The cohort Shapley (CS) method is model-free but has exponential cost in the dimension of the input space. A supervised on-manifold Shapley method from Frye et al. (2020) is also model free but requires as input a second black box model that has to be trained for the Shapley value problem. We introduce an integrated gradient (IG) version of cohort Shapley, called IGCS, with cost O(nd). We show that over the vast majority of the relevant unit cube that the IGCS value function is close to a multilinear function for which IGCS matches CS. Another benefit of IGCS is that is allows IG methods to be used with binary predictors. We use some area between curves (ABC) measures to quantify the performance of IGCS. On a problem from high energy physics we verify that IGCS has nearly the same ABCs as CS does. We also use it on a problem from computational chemistry in 1024 variables. We see there that IGCS attains much higher ABCs than we get from Monte Carlo sampling. The code is publicly available at https://github.com/cohortshapley/cohortintgrad