# Exact Functional ANOVA Decomposition for Categorical Inputs Models

arXiv: https://arxiv.org/abs/2603.02673 · HTML: https://mlsanity.com/paper/2603.02673/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 32 references that are in the map.
- First posted on arXiv 3 Mar 2026.

## Builds on (most cited first, 14 of 14)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Quantifying Attention Flow in Transformers](https://mlsanity.com/paper/2005.00928/) (2020)
- [Revisiting Deep Learning Models for Tabular Data](https://mlsanity.com/paper/2106.11959/) (2021)
- [Variational Autoencoders and Nonlinear ICA: A Unifying Framework](https://mlsanity.com/paper/1907.04809/) (2019)
- [The many Shapley values for model explanation](https://mlsanity.com/paper/1908.08474/) (2019)
- [Consistent Individualized Feature Attribution for Tree Ensembles](https://mlsanity.com/paper/1802.03888/) (2018)
- [Feature relevance quantification in explainable AI: A causal problem](https://mlsanity.com/paper/1910.13413/) (2019)
- [On the Tractability of SHAP Explanations](https://mlsanity.com/paper/2009.08634/) (2020)
- [Quantifying & Modeling Multimodal Interactions: An Information Decomposition Framework](https://mlsanity.com/paper/2302.12247/) (2023)
- [Purifying Interaction Effects with the Functional ANOVA: An Efficient Algorithm for Recovering Identifiable Additive Models](https://mlsanity.com/paper/1911.04974/) (2019)
- [SHAP values via sparse Fourier representation](https://mlsanity.com/paper/2410.06300/) (2024)
- [A benchmark of categorical encoders for binary classification](https://mlsanity.com/paper/2307.09191/) (2023)
- [Tree Ensemble Explainability through the Hoeffding Functional Decomposition and TreeHFD Algorithm](https://mlsanity.com/paper/2510.24815/) (2025)

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

- [Generalized Functional ANOVA: A Complete Theoretical Framework](https://mlsanity.com/paper/2605.18422/) (2026)

## Abstract (arXiv)

Functional ANOVA offers a principled framework for interpretability by decomposing a model's prediction into main effects and higher-order interactions. For independent features, this decomposition is well-defined, strongly linked with SHAP values, and serves as a cornerstone of additive explainability. However, the lack of an explicit closed-form expression for general dependent distributions has forced practitioners to rely on costly sampling-based approximations. We completely resolve this limitation for categorical inputs. By bridging functional analysis with the extension of discrete Fourier analysis, we derive a closed-form decomposition without any assumption. Our formulation is computationally very efficient. It seamlessly recovers the classical independent case and extends to arbitrary dependence structures, including distributions with non-rectangular support. Furthermore, leveraging the intrinsic link between SHAP and ANOVA under independence, our framework yields a natural generalization of SHAP values for the general categorical setting.