# Shapley Sets: Feature Attribution via Recursive Function Decomposition

arXiv: https://arxiv.org/abs/2307.01777 · HTML: https://mlsanity.com/paper/2307.01777/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 19 references that are in the map.
- First posted on arXiv 4 Jul 2023.

## Builds on (most cited first, 11 of 11)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [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)
- [Feature relevance quantification in explainable AI: A causal problem](https://mlsanity.com/paper/1910.13413/) (2019)
- [Asymmetric Shapley values: incorporating causal knowledge into model-agnostic explainability](https://mlsanity.com/paper/1910.06358/) (2019)
- [Causal Shapley Values: Exploiting Causal Knowledge to Explain Individual Predictions of Complex Models](https://mlsanity.com/paper/2011.01625/) (2020)
- [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)
- [groupShapley: Efficient prediction explanation with Shapley values for feature groups](https://mlsanity.com/paper/2106.12228/) (2021)
- [Evaluating Feature Attribution Methods in the Image Domain](https://mlsanity.com/paper/2202.12270/) (2022)
- [Hodge decomposition and the Shapley value of a cooperative game](https://mlsanity.com/paper/1709.08318/) (2017)

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

- [Succinct Interaction-Aware Explanations](https://mlsanity.com/paper/2402.05566/) (2024)
- [SX-GeoTree: Self-eXplaining Geospatial Regression Tree Incorporating the Spatial Similarity of Feature Attributions](https://mlsanity.com/paper/2511.19845/) (2025)

## Abstract (arXiv)

Despite their ubiquitous use, Shapley value feature attributions can be misleading due to feature interaction in both model and data. We propose an alternative attribution approach, Shapley Sets, which awards value to sets of features. Shapley Sets decomposes the underlying model into non-separable variable groups using a recursive function decomposition algorithm with log linear complexity in the number of variables. Shapley Sets attributes to each non-separable variable group their combined value for a particular prediction. We show that Shapley Sets is equivalent to the Shapley value over the transformed feature set and thus benefits from the same axioms of fairness. Shapley Sets is value function agnostic and we show theoretically and experimentally how Shapley Sets avoids pitfalls associated with Shapley value based alternatives and are particularly advantageous for data types with complex dependency structure.