mlsanityData to 14 Oct 2026

Purifying Interaction Effects with the Functional ANOVA: An Efficient Algorithm for Recovering Identifiable Additive Models

arXiv 1911.04974 ↗First posted 12 Nov 2019stat.ML cs.AI cs.LGcited by 42

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Abstract (arXiv)

Models which estimate main effects of individual variables alongside interaction effects have an identifiability challenge: effects can be freely moved between main effects and interaction effects without changing the model prediction. This is a critical problem for interpretability because it permits "contradictory" models to represent the same function. To solve this problem, we propose pure interaction effects: variance in the outcome which cannot be represented by any smaller subset of features. This definition has an equivalence with the Functional ANOVA decomposition. To compute this decomposition, we present a fast, exact algorithm that transforms any piecewise-constant function (such as a tree-based model) into a purified, canonical representation. We apply this algorithm to Generalized Additive Models with interactions trained on several datasets and show large disparity, including contradictions, between the effects before and after purification. These results underscore the need to specify data distributions and ensure identifiability before interpreting model parameters.

Key facts. Cited by 42 papers in the map (data through 14 Oct 2026). First posted on arXiv 12 Nov 2019.

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Citing papers per year: 2021: 3; 2022: 4; 2023: 5; 2024: 11; 2025: 11; 2026: 8.

42 papers.

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  1. 2021NODE-GAM: Neural Generalized Additive Model for Interpretable Deep Learningcited by 88
  2. 2022From Shapley Values to Generalized Additive Models and backcited by 60
  3. 2024Beyond TreeSHAP: Efficient Computation of Any-Order Shapley Interactions for Tree Ensemblescited by 31
  4. 2024KernelSHAP-IQ: Weighted Least-Square Optimization for Shapley Interactionscited by 22
  5. 2022Unifying local and global model explanations by functional decomposition of low dimensional structurescited by 18
  6. 2021PredDiff: Explanations and Interactions from Conditional Expectationscited by 17
  7. 2024Towards a theory of model distillationcited by 15
  8. 2021Towards Rigorous Interpretations: a Formalisation of Feature Attributioncited by 11
  9. 2023A New PHO-rmula for Improved Performance of Semi-Structured Networkscited by 11
  10. 2022Ultra-marginal Feature Importance: Learning from Data with Causal Guaranteescited by 6
  11. 2023Interpretable Survival Analysis for Heart Failure Risk Predictioncited by 6
  12. 2025Tree Ensemble Explainability through the Hoeffding Functional Decomposition and TreeHFD Algorithmcited by 6
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  1. 2023PiML Toolbox for Interpretable Machine Learning Model Development and Diagnosticscited by 4
  2. 2023Interpretable Machine Learning based on Functional ANOVA Framework: Algorithms and Comparisonscited by 4
  3. 2023Contextualized Machine Learningcited by 4
  4. 2024Fast Estimation of Partial Dependence Functions using Treescited by 4
  5. 2024Disentangling Interactions and Dependencies in Feature Attributioncited by 4
  6. 2025Tensor Product Neural Networks for Functional ANOVA Modelcited by 4
  7. 2022Using Model-Based Trees with Boosting to Fit Low-Order Functional ANOVA Modelscited by 3
  8. 2024NeurCAM: Interpretable Neural Clustering via Additive Modelscited by 3
  9. 2024Interpretable Prediction and Feature Selection for Survival Analysiscited by 2
  10. 2024META-ANOVA: Screening interactions for interpretable machine learningcited by 2
  11. 2024Inherently Interpretable Tree Ensemble Learningcited by 2
  12. 2024Function Trees: Transparent Machine Learningcited by 1
  13. 2024DNAMite: Interpretable Calibrated Survival Analysis with Discretized Additive Modelscited by 1
  14. 2025Common Functional Decompositions Can Mis-attribute Differences in Outcomes Between Populationscited by 1
  15. 2025The Most Important Features in Generalized Additive Models Might Be Groups of Featurescited by 1
  16. 2025STRIDE: Subset-Free Functional Decomposition for XAI in Tabular Settingscited by 1
  17. 2026Exact Functional ANOVA Decomposition for Categorical Inputs Modelscited by 1
  18. 2026Generalized Functional ANOVA: A Complete Theoretical Frameworkcited by 1
  19. 2026Hoeffding Concept Bottleneck Models with Applications to Overhead Imagescited by 1
  20. 2025dnamite: A Python Package for Neural Additive Modelscited by 0
  21. 2025Explainable Boosting Machine for Predicting Claim Severity and Frequency in Car Insurancecited by 0
  22. 2025CUBE: Contrastive Understanding by Balanced Experimentscited by 0
  23. 2025Bayesian Neural Networks for Functional ANOVA modelcited by 0
  24. 2025Fourier Analysis on the Boolean Hypercube via Hoeffding Functional Decompositioncited by 0
  25. 2025Layer-Wise Modality Decomposition for Interpretable Multimodal Sensor Fusioncited by 0
  26. 2026Statistical Inference for Explainable Boosting Machinescited by 0
  27. 2026Do covariates explain why these groups differ? The choice of reference group can reverse conclusions in the Oaxaca-Blinder decompositioncited by 0
  28. 2026The Quadrilateral Loss: Additivity as a Measurable Behavior of Dense Neural Networkscited by 0
  29. 2026Minimax Additive Regression under Unknown Dependent Designscited by 0
  30. 2026Explaining Heterogeneous Treatment Effects with Causal Forests and the Hoeffding Functional Decompositioncited by 0