# Functional relevance based on the continuous Shapley value

arXiv: https://arxiv.org/abs/2411.18575 · HTML: https://mlsanity.com/paper/2411.18575/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 50 references that are in the map.
- First posted on arXiv 27 Nov 2024.

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

- [Explainable Artificial Intelligence (XAI): Concepts, Taxonomies, Opportunities and Challenges toward Responsible AI](https://mlsanity.com/paper/1910.10045/) (2019)
- [Controlling the false discovery rate via knockoffs](https://mlsanity.com/paper/1404.5609/) (2014)
- [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)
- [A knockoff filter for high-dimensional selective inference](https://mlsanity.com/paper/1602.03574/) (2016)
- [Deep Learning for Functional Data Analysis with Adaptive Basis Layers](https://mlsanity.com/paper/2106.10414/) (2021)
- [Non-linear Functional Modeling using Neural Networks](https://mlsanity.com/paper/2104.09371/) (2021)
- [scikit-fda: A Python Package for Functional Data Analysis](https://mlsanity.com/paper/2211.02566/) (2022)
- [Functional Neural Networks: Shift invariant models for functional data with applications to EEG classification](https://mlsanity.com/paper/2301.05869/) (2023)
- [The mRMR variable selection method: a comparative study for functional data](https://mlsanity.com/paper/1507.03496/) (2015)
- [Understanding complex predictive models with Ghost Variables](https://mlsanity.com/paper/1912.06407/) (2019)
- [Functional Data Analysis: An Introduction and Recent Developments](https://mlsanity.com/paper/2312.05523/) (2023)

## Built on by (most cited first, 1 of 1)

- [OperatorSHAP: Fast and Accurate Shapley Value Estimation for Neural Operators](https://mlsanity.com/paper/2606.28065/) (2026)

## Abstract (arXiv)

The presence of artificial intelligence (AI) in our society is increasing, which brings with it the need to understand the behavior of AI mechanisms, including machine learning predictive algorithms fed with tabular data, text or images, among others. This work focuses on interpretability of predictive models based on functional data. Designing interpretability methods for functional data models implies working with a set of features whose size is infinite. In the context of scalar on function regression, we propose an interpretability method based on the Shapley value for continuous games, a mathematical formulation that allows for the fair distribution of a global payoff among a continuous set of players. The method is illustrated through a set of experiments with simulated and real data sets. The open source Python package ShapleyFDA is also presented.