# Cooperative effects in feature importance of individual patterns: application to air pollutants and Alzheimer disease

arXiv: https://arxiv.org/abs/2508.00930 · HTML: https://mlsanity.com/paper/2508.00930/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 23 references that are in the map.
- First posted on arXiv 30 Jul 2025.

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

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [The physics of higher-order interactions in complex systems](https://mlsanity.com/paper/2110.06023/) (2021)
- [Quantifying High-order Interdependencies via Multivariate Extensions of the Mutual Information](https://mlsanity.com/paper/1902.11239/) (2019)
- [Exploration of synergistic and redundant information sharing in static and dynamical Gaussian systems](https://mlsanity.com/paper/1411.2832/) (2014)
- [Quantifying dynamical high-order interdependencies from the O-information: an application to neural spiking dynamics](https://mlsanity.com/paper/2007.16018/) (2020)
- [A simple algorithm for global sensitivity analysis with Shapley effects](https://mlsanity.com/paper/2009.00874/) (2020)
- [Assessing high-order effects in feature importance via predictability decomposition](https://mlsanity.com/paper/2412.09964/) (2024)
- [Local Granger Causality](https://mlsanity.com/paper/2010.13833/) (2020)

## Abstract (arXiv)

Leveraging recent advances in the analysis of synergy and redundancy in systems of random variables, an adaptive version of the widely used metric Leave One Covariate Out (LOCO) has been recently proposed to quantify cooperative effects in feature importance (Hi-Fi), a key technique in explainable artificial intelligence (XAI), so as to disentangle high-order effects involving a particular input feature in regression problems. Differently from standard feature importance tools, where a single score measures the relevance of each feature, each feature is here characterized by three scores, a two-body (unique) score and higher-order scores (redundant and synergistic). This paper presents a framework to assign those three scores (unique, redundant, and synergistic) to each individual pattern of the data set, while comparing it with the well-known measure of feature importance named it Shapley effect. To illustrate the potential of the proposed framework, we focus on a One-Health application: the relation between air pollutants and Alzheimer's disease mortality rate. Our main result is the synergistic association between features related to O3 and NO2 with mortality, especially in the provinces of Bergamo e Brescia; notably also the density of urban green areas displays synergistic influence with pollutants for the prediction of AD mortality. Our results place local Hi-Fi as a promising tool of wide applicability, which opens new perspectives for XAI as well as to analyze high-order relationships in complex systems.