Generalized Functional ANOVA in Closed-Form: A Unified View of Additive Explanations

2026-05-19 · Source: stat.ML updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Data Science & Analytics · Depth: Expert, quick

Summary

A new paper submitted on May 18, 2026, titled "Generalized Functional ANOVA in Closed-Form: A Unified View of Additive Explanations," addresses the challenge of obtaining a tractable representation and estimating the functional ANOVA decomposition for dependent continuous inputs. This decomposition, also known as Hoeffding decomposition, is a fundamental tool for additive explainability, connecting to SHAP values, generalized additive models, and orthogonal polynomial expansions. The authors, Baptiste Ferrere, Nicolas Bousquet, Fabrice Gamboa, and Jean-Michel Loubes, combine Hilbert space methods with generalized functional ANOVA to construct an explicit Riesz Basis, enabling easy computation of the decomposition. Their formulation recovers the classical independent case and its associated orthogonal decomposition. The work proposes a model-agnostic algorithm to estimate the decomposition from data, demonstrating its effectiveness against state-of-the-art explanation methods.

Key takeaway

For research scientists and AI engineers focused on model interpretability, this work offers a robust, explicit method for functional ANOVA decomposition, even with dependent inputs. You can leverage this approach to gain deeper insights into model predictions by accurately separating main effects from higher-order interactions, which is crucial for understanding complex machine learning models. Consider integrating this algorithm to enhance the explainability of your continuous input models.

Key insights

A new method provides a tractable, explicit functional ANOVA decomposition for dependent continuous inputs, enhancing model interpretability.

Principles

• Functional ANOVA decomposes model predictions into main and interaction effects.
• Hilbert space methods enable explicit decomposition for dependent inputs.

Method

The proposed method combines Hilbert space techniques with generalized functional ANOVA to build an explicit Riesz Basis, allowing for direct computation and estimation of the decomposition from data in a model-agnostic manner.

In practice

• Apply for model-agnostic interpretability.
• Use to compute main effects and interactions.

Topics

• Functional ANOVA
• Additive Explanations
• Dependent Inputs
• Hilbert Space Methods
• Riesz Basis

Best for: Research Scientist, AI Engineer, AI Scientist, Machine Learning Engineer, Data Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by stat.ML updates on arXiv.org.