# On the coalitional decomposition of parameters of interest

arXiv: https://arxiv.org/abs/2301.02539 · HTML: https://mlsanity.com/paper/2301.02539/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Jan 2023.

## Built on by (most cited first, 7 of 7)

- [A Holistic Approach to Unifying Automatic Concept Extraction and Concept Importance Estimation](https://mlsanity.com/paper/2306.07304/) (2023)
- [Unlocking Feature Visualization for Deeper Networks with MAgnitude Constrained Optimization](https://mlsanity.com/paper/2306.06805/) (2023)
- [Saliency strikes back: How filtering out high frequencies improves white-box explanations](https://mlsanity.com/paper/2307.09591/) (2023)
- [Beyond Shapley Values: Cooperative Games for the Interpretation of Machine Learning Models](https://mlsanity.com/paper/2506.13900/) (2025)
- [Hoeffding decomposition of black-box models with dependent inputs](https://mlsanity.com/paper/2310.06567/) (2023)
- [A new paradigm for global sensitivity analysis](https://mlsanity.com/paper/2409.06271/) (2024)
- [Fourier Analysis on the Boolean Hypercube via Hoeffding Functional Decomposition](https://mlsanity.com/paper/2510.07088/) (2025)

## Abstract (arXiv)

Understanding the behavior of a black-box model with probabilistic inputs can be based on the decomposition of a parameter of interest (e.g., its variance) into contributions attributed to each coalition of inputs (i.e., subsets of inputs). In this paper, we produce conditions for obtaining unambiguous and interpretable decompositions of very general parameters of interest. This allows to recover known decompositions, holding under weaker assumptions than stated in the literature.