# From SHAP Scores to Feature Importance Scores

arXiv: https://arxiv.org/abs/2405.11766 · HTML: https://mlsanity.com/paper/2405.11766/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 57 references that are in the map.
- First posted on arXiv 20 May 2024.

## Builds on (most cited first, 9 of 9)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Methods for Interpreting and Understanding Deep Neural Networks](https://mlsanity.com/paper/1706.07979/) (2017)
- [On the Tractability of SHAP Explanations](https://mlsanity.com/paper/2009.08634/) (2020)
- [Logic-Based Explainability in Machine Learning](https://mlsanity.com/paper/2211.00541/) (2022)
- [On the Complexity of SHAP-Score-Based Explanations: Tractability via Knowledge Compilation and Non-Approximability Results](https://mlsanity.com/paper/2104.08015/) (2021)
- [The Inadequacy of Shapley Values for Explainability](https://mlsanity.com/paper/2302.08160/) (2023)
- [Disproving XAI Myths with Formal Methods -- Initial Results](https://mlsanity.com/paper/2306.01744/) (2023)
- [On Formal Feature Attribution and Its Approximation](https://mlsanity.com/paper/2307.03380/) (2023)
- [Refutation of Shapley Values for XAI -- Additional Evidence](https://mlsanity.com/paper/2310.00416/) (2023)

## Built on by (most cited first, 8 of 8)

- [Logic-Based Explainability: Past, Present & Future](https://mlsanity.com/paper/2406.11873/) (2024)
- [SHAP scores fail pervasively even when Lipschitz succeeds](https://mlsanity.com/paper/2412.13866/) (2024)
- [Efficient Contrastive Explanations on Demand](https://mlsanity.com/paper/2412.18262/) (2024)
- [The Explanation Game -- Rekindled (Extended Version)](https://mlsanity.com/paper/2501.11429/) (2025)
- [Binary Spiking Neural Networks as Causal Models](https://mlsanity.com/paper/2604.27007/) (2026)
- [The Sets of Power](https://mlsanity.com/paper/2410.07867/) (2024)
- [Feature-Guided Neighbor Selection for Non-Expert Evaluation of Model Predictions](https://mlsanity.com/paper/2507.06029/) (2025)
- [Efficient & Correct Predictive Equivalence for Decision Trees](https://mlsanity.com/paper/2509.17774/) (2025)

## Abstract (arXiv)

A central goal of eXplainable Artificial Intelligence (XAI) is to assign relative importance to the features of a Machine Learning (ML) model given some prediction. The importance of this task of explainability by feature attribution is illustrated by the ubiquitous recent use of tools such as SHAP and LIME. Unfortunately, the exact computation of feature attributions, using the game-theoretical foundation underlying SHAP and LIME, can yield manifestly unsatisfactory results, that tantamount to reporting misleading relative feature importance. Recent work targeted rigorous feature attribution, by studying axiomatic aggregations of features based on logic-based definitions of explanations by feature selection. This paper shows that there is an essential relationship between feature attribution and a priori voting power, and that those recently proposed axiomatic aggregations represent a few instantiations of the range of power indices studied in the past. Furthermore, it remains unclear how some of the most widely used power indices might be exploited as feature importance scores (FISs), i.e. the use of power indices in XAI, and which of these indices would be the best suited for the purposes of XAI by feature attribution, namely in terms of not producing results that could be deemed as unsatisfactory. This paper proposes novel desirable properties that FISs should exhibit. In addition, the paper also proposes novel FISs exhibiting the proposed properties. Finally, the paper conducts a rigorous analysis of the best-known power indices in terms of the proposed properties.