# Factor Importance Ranking and Selection using Total Indices

arXiv: https://arxiv.org/abs/2401.00800 · HTML: https://mlsanity.com/paper/2401.00800/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 103 references that are in the map.
- First posted on arXiv 1 Jan 2024.

## Builds on (most cited first, 18 of 18)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [A Benchmark for Interpretability Methods in Deep Neural Networks](https://mlsanity.com/paper/1806.10758/) (2018)
- [All Models are Wrong, but Many are Useful: Learning a Variable's Importance by Studying an Entire Class of Prediction Models Simultaneously](https://mlsanity.com/paper/1801.01489/) (2018)
- [Interpretable machine learning: definitions, methods, and applications](https://mlsanity.com/paper/1901.04592/) (2019)
- [ranger: A Fast Implementation of Random Forests for High Dimensional Data in C++ and R](https://mlsanity.com/paper/1508.04409/) (2015)
- [Unrestricted Permutation forces Extrapolation: Variable Importance Requires at least One More Model, or There Is No Free Variable Importance](https://mlsanity.com/paper/1905.03151/) (2019)
- [Efficient nonparametric statistical inference on population feature importance using Shapley values](https://mlsanity.com/paper/2006.09481/) (2020)
- [A general framework for inference on algorithm-agnostic variable importance](https://mlsanity.com/paper/2004.03683/) (2020)
- [A simple measure of conditional dependence](https://mlsanity.com/paper/1910.12327/) (2019)
- [Feature Importance Ranking for Deep Learning](https://mlsanity.com/paper/2010.08973/) (2020)
- [Feature Importance: A Closer Look at Shapley Values and LOCO](https://mlsanity.com/paper/2303.05981/) (2023)
- [Kernel Partial Correlation Coefficient -- a Measure of Conditional Dependence](https://mlsanity.com/paper/2012.14804/) (2020)
- [Nonparametric Feature Impact and Importance](https://mlsanity.com/paper/2006.04750/) (2020)
- [Variable importance without impossible data](https://mlsanity.com/paper/2205.15750/) (2022)
- [Model free variable importance for high dimensional data](https://mlsanity.com/paper/2211.08414/) (2022)

## Built on by (most cited first, 2 of 2)

- [Trustworthy Feature Importance Avoids Unrestricted Permutations](https://mlsanity.com/paper/2604.11253/) (2026)
- [Psi-Resilience: Model-Free Feature Importance from 1D Topological Signals](https://mlsanity.com/paper/2610.02299/) (2026)

## Abstract (arXiv)

Factor importance measures the impact of each feature on output prediction accuracy. Many existing works focus on the model-based importance, but an important feature in one learning algorithm may hold little significance in another model. Hence, a factor importance measure ought to characterize the feature's predictive potential without relying on a specific prediction algorithm. Such algorithm-agnostic importance is termed as intrinsic importance in Williamson et al. (2023), but their estimator again requires model fitting. To bypass the modeling step, we present the equivalence between predictiveness potential and total Sobol' indices from global sensitivity analysis, and introduce a novel consistent estimator that can be directly estimated from noisy data. Integrating with forward selection and backward elimination gives rise to FIRST, Factor Importance Ranking and Selection using Total (Sobol') indices. Extensive simulations are provided to demonstrate the effectiveness of FIRST on regression and binary classification problems, and a clear advantage over the state-of-the-art methods.