# High Dimensional Model Explanations: an Axiomatic Approach

arXiv: https://arxiv.org/abs/2006.08969 · HTML: https://mlsanity.com/paper/2006.08969/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Jun 2020.

## Built on by (most cited first, 13 of 13)

- [Data Banzhaf: A Robust Data Valuation Framework for Machine Learning](https://mlsanity.com/paper/2205.15466/) (2022)
- [shapiq: Shapley Interactions for Machine Learning](https://mlsanity.com/paper/2410.01649/) (2024)
- [DualCF: Efficient Model Extraction Attack from Counterfactual Explanations](https://mlsanity.com/paper/2205.06504/) (2022)
- [Beyond TreeSHAP: Efficient Computation of Any-Order Shapley Interactions for Tree Ensembles](https://mlsanity.com/paper/2401.12069/) (2024)
- [Joint Shapley values: a measure of joint feature importance](https://mlsanity.com/paper/2107.11357/) (2021)
- [Axiomatic Aggregations of Abductive Explanations](https://mlsanity.com/paper/2310.03131/) (2023)
- [Improved Feature Importance Computations for Tree Models: Shapley vs. Banzhaf](https://mlsanity.com/paper/2108.04126/) (2021)
- [Towards Unified Attribution in Explainable AI, Data-Centric AI, and Mechanistic Interpretability](https://mlsanity.com/paper/2501.18887/) (2025)
- [Prediction via Shapley Value Regression](https://mlsanity.com/paper/2505.04775/) (2025)
- [Kernel Banzhaf: A Fast and Robust Estimator for Banzhaf Values](https://mlsanity.com/paper/2410.08336/) (2024)
- [Model Explanations via the Axiomatic Causal Lens](https://mlsanity.com/paper/2109.03890/) (2021)
- [IMACS: Image Model Attribution Comparison Summaries](https://mlsanity.com/paper/2201.11196/) (2022)
- [Rigorous Feature Importance Scores based on Shapley Value and Banzhaf Index](https://mlsanity.com/paper/2508.11959/) (2025)

## Abstract (arXiv)

Complex black-box machine learning models are regularly used in critical decision-making domains. This has given rise to several calls for algorithmic explainability. Many explanation algorithms proposed in literature assign importance to each feature individually. However, such explanations fail to capture the joint effects of sets of features. Indeed, few works so far formally analyze high-dimensional model explanations. In this paper, we propose a novel high dimension model explanation method that captures the joint effect of feature subsets. We propose a new axiomatization for a generalization of the Banzhaf index; our method can also be thought of as an approximation of a black-box model by a higher-order polynomial. In other words, this work justifies the use of the generalized Banzhaf index as a model explanation by showing that it uniquely satisfies a set of natural desiderata and that it is the optimal local approximation of a black-box model. Our empirical evaluation of our measure highlights how it manages to capture desirable behavior, whereas other measures that do not satisfy our axioms behave in an unpredictable manner.