# Variable Importance Clouds: A Way to Explore Variable Importance for the Set of Good Models

arXiv: https://arxiv.org/abs/1901.03209 · HTML: https://mlsanity.com/paper/1901.03209/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Jan 2019.

## Built on by (most cited first, 19 of 19)

- [Characterizing Fairness Over the Set of Good Models Under Selective Labels](https://mlsanity.com/paper/2101.00352/) (2021)
- [Directional Bias Amplification](https://mlsanity.com/paper/2102.12594/) (2021)
- [Predictive Multiplicity in Probabilistic Classification](https://mlsanity.com/paper/2206.01131/) (2022)
- [Loss-Aversively Fair Classification](https://mlsanity.com/paper/2105.04273/) (2021)
- [Systemizing Multiplicity: The Curious Case of Arbitrariness in Machine Learning](https://mlsanity.com/paper/2501.14959/) (2025)
- [Recourse under Model Multiplicity via Argumentative Ensembling (Technical Report)](https://mlsanity.com/paper/2312.15097/) (2023)
- [Predictive Churn with the Set of Good Models](https://mlsanity.com/paper/2402.07745/) (2024)
- [Partial Order in Chaos: Consensus on Feature Attributions in the Rashomon Set](https://mlsanity.com/paper/2110.13369/) (2021)
- [Multi-Target Multiplicity: Flexibility and Fairness in Target Specification under Resource Constraints](https://mlsanity.com/paper/2306.13738/) (2023)
- [A Guide to Feature Importance Methods for Scientific Inference](https://mlsanity.com/paper/2404.12862/) (2024)
- [Be Intentional About Fairness!: Fairness, Size, and Multiplicity in the Rashomon Set](https://mlsanity.com/paper/2501.15634/) (2025)
- [Bayesian subset selection and variable importance for interpretable prediction and classification](https://mlsanity.com/paper/2104.10150/) (2021)
- [On the Trustworthiness of Tree Ensemble Explainability Methods](https://mlsanity.com/paper/2110.00086/) (2021)
- [Subset selection for linear mixed models](https://mlsanity.com/paper/2107.12890/) (2021)
- [Argumentative Ensembling for Robust Recourse under Model Multiplicity](https://mlsanity.com/paper/2506.20260/) (2025)
- [Accounting for Model Uncertainty in Algorithmic Discrimination](https://mlsanity.com/paper/2105.04249/) (2021)
- [A Computational Exploration of Emerging Methods of Variable Importance Estimation](https://mlsanity.com/paper/2208.03373/) (2022)
- [Reconciling Predictive Multiplicity in Practice](https://mlsanity.com/paper/2501.16549/) (2025)
- [VAR: Visual Analysis for Rashomon Set of Machine Learning Models' Performance](https://mlsanity.com/paper/2507.22556/) (2025)

## Abstract (arXiv)

Variable importance is central to scientific studies, including the social sciences and causal inference, healthcare, and other domains. However, current notions of variable importance are often tied to a specific predictive model. This is problematic: what if there were multiple well-performing predictive models, and a specific variable is important to some of them and not to others? In that case, we may not be able to tell from a single well-performing model whether a variable is always important in predicting the outcome. Rather than depending on variable importance for a single predictive model, we would like to explore variable importance for all approximately-equally-accurate predictive models. This work introduces the concept of a variable importance cloud, which maps every variable to its importance for every good predictive model. We show properties of the variable importance cloud and draw connections to other areas of statistics. We introduce variable importance diagrams as a projection of the variable importance cloud into two dimensions for visualization purposes. Experiments with criminal justice, marketing data, and image classification tasks illustrate how variables can change dramatically in importance for approximately-equally-accurate predictive models