# SHAP-IQ: Unified Approximation of any-order Shapley Interactions

arXiv: https://arxiv.org/abs/2303.01179 · HTML: https://mlsanity.com/paper/2303.01179/

## Key facts

- Cited by 51 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 54 references that are in the map.
- First posted on arXiv 2 Mar 2023.

## Builds on (most cited first, 24 of 24)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [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)
- [DistilBERT, a distilled version of BERT: smaller, faster, cheaper and lighter](https://mlsanity.com/paper/1910.01108/) (2019)
- [Data Shapley: Equitable Valuation of Data for Machine Learning](https://mlsanity.com/paper/1904.02868/) (2019)
- [Datasets: A Community Library for Natural Language Processing](https://mlsanity.com/paper/2109.02846/) (2021)
- [Towards Efficient Data Valuation Based on the Shapley Value](https://mlsanity.com/paper/1902.10275/) (2019)
- [Explaining by Removing: A Unified Framework for Model Explanation](https://mlsanity.com/paper/2011.14878/) (2020)
- [Representer Point Selection for Explaining Deep Neural Networks](https://mlsanity.com/paper/1811.09720/) (2018)
- [Improving KernelSHAP: Practical Shapley Value Estimation via Linear Regression](https://mlsanity.com/paper/2012.01536/) (2020)
- [The Shapley Taylor Interaction Index](https://mlsanity.com/paper/1902.05622/) (2019)
- [Algorithms to estimate Shapley value feature attributions](https://mlsanity.com/paper/2207.07605/) (2022)
- [Explaining Explanations: Axiomatic Feature Interactions for Deep Networks](https://mlsanity.com/paper/2002.04138/) (2020)
- [Detecting Statistical Interactions from Neural Network Weights](https://mlsanity.com/paper/1705.04977/) (2017)
- [How does this interaction affect me? Interpretable attribution for feature interactions](https://mlsanity.com/paper/2006.10965/) (2020)
- [Faith-Shap: The Faithful Shapley Interaction Index](https://mlsanity.com/paper/2203.00870/) (2022)
- [Beyond Word Importance: Contextual Decomposition to Extract Interactions from LSTMs](https://mlsanity.com/paper/1801.05453/) (2018)
- [Hierarchical interpretations for neural network predictions](https://mlsanity.com/paper/1806.05337/) (2018)
- [TalkToModel: Explaining Machine Learning Models with Interactive Natural Language Conversations](https://mlsanity.com/paper/2207.04154/) (2022)
- [Efficient nonparametric statistical inference on population feature importance using Shapley values](https://mlsanity.com/paper/2006.09481/) (2020)
- [From Shapley Values to Generalized Additive Models and back](https://mlsanity.com/paper/2209.04012/) (2022)
- [Bounding the Estimation Error of Sampling-based Shapley Value Approximation](https://mlsanity.com/paper/1306.4265/) (2013)
- [Feature Interaction Interpretability: A Case for Explaining Ad-Recommendation Systems via Neural Interaction Detection](https://mlsanity.com/paper/2006.10966/) (2020)
- [Quantifying Model Complexity via Functional Decomposition for Better Post-Hoc Interpretability](https://mlsanity.com/paper/1904.03867/) (2019)

## Built on by (most cited first, 30 of 51)

- [shapiq: Shapley Interactions for Machine Learning](https://mlsanity.com/paper/2410.01649/) (2024)
- [Beyond TreeSHAP: Efficient Computation of Any-Order Shapley Interactions for Tree Ensembles](https://mlsanity.com/paper/2401.12069/) (2024)
- [KernelSHAP-IQ: Weighted Least-Square Optimization for Shapley Interactions](https://mlsanity.com/paper/2405.10852/) (2024)
- [Stochastic Amortization: A Unified Approach to Accelerate Feature and Data Attribution](https://mlsanity.com/paper/2401.15866/) (2024)
- [ProxySPEX: Inference-Efficient Interpretability via Sparse Feature Interactions in LLMs](https://mlsanity.com/paper/2505.17495/) (2025)
- [Learning to Understand: Identifying Interactions via the M"obius Transform](https://mlsanity.com/paper/2402.02631/) (2024)
- [Exact Computation of Any-Order Shapley Interactions for Graph Neural Networks](https://mlsanity.com/paper/2501.16944/) (2025)
- [SPEX: Scaling Feature Interaction Explanations for LLMs](https://mlsanity.com/paper/2502.13870/) (2025)
- [Unifying Feature-Based Explanations with Functional ANOVA and Cooperative Game Theory](https://mlsanity.com/paper/2412.17152/) (2024)
- [Explaining Text Similarity in Transformer Models](https://mlsanity.com/paper/2405.06604/) (2024)
- [One Sample Fits All: Approximating All Probabilistic Values Simultaneously and Efficiently](https://mlsanity.com/paper/2410.23808/) (2024)
- [Feature Responsiveness Scores: Model-Agnostic Explanations for Recourse](https://mlsanity.com/paper/2410.22598/) (2024)
- [SHAP Meets Tensor Networks: Provably Tractable Explanations with Parallelism](https://mlsanity.com/paper/2510.21599/) (2025)
- [PolySHAP: Extending KernelSHAP with Interaction-Informed Polynomial Regression](https://mlsanity.com/paper/2601.18608/) (2026)
- [Explaining Similarity in Vision-Language Encoders with Weighted Banzhaf Interactions](https://mlsanity.com/paper/2508.05430/) (2025)
- [Position: We Need An Algorithmic Understanding of Generative AI](https://mlsanity.com/paper/2507.07544/) (2025)
- [An Odd Estimator for Shapley Values](https://mlsanity.com/paper/2602.01399/) (2026)
- [Efficient and Accurate Explanation Estimation with Distribution Compression](https://mlsanity.com/paper/2406.18334/) (2024)
- [SHAP zero Explains Biological Sequence Models with Near-zero Marginal Cost for Future Queries](https://mlsanity.com/paper/2410.19236/) (2024)
- [Disentangling Interactions and Dependencies in Feature Attribution](https://mlsanity.com/paper/2410.23772/) (2024)
- [SurvBeX: An explanation method of the machine learning survival models based on the Beran estimator](https://mlsanity.com/paper/2308.03730/) (2023)
- [Explaining Caption-Image Interactions in CLIP Models with Second-Order Attributions](https://mlsanity.com/paper/2408.14153/) (2024)
- [Exactly Computing do-Shapley Values](https://mlsanity.com/paper/2602.07203/) (2026)
- [Shapley Value Approximation Based on k-Additive Games](https://mlsanity.com/paper/2502.04763/) (2025)
- [Adaptive Prompting: Ad-hoc Prompt Composition for Social Bias Detection](https://mlsanity.com/paper/2502.06487/) (2025)
- [EvalxNLP: A Framework for Benchmarking Post-Hoc Explainability Methods on NLP Models](https://mlsanity.com/paper/2505.01238/) (2025)
- [Quadrature-TreeSHAP: Depth-Independent TreeSHAP and Shapley Interactions](https://mlsanity.com/paper/2605.04497/) (2026)
- [Using Shapley interactions to understand how models use structure](https://mlsanity.com/paper/2403.13106/) (2024)
- [Energy-Based Model for Accurate Estimation of Shapley Values in Feature Attribution](https://mlsanity.com/paper/2404.01078/) (2024)
- [Data Science Principles for Interpretable and Explainable AI](https://mlsanity.com/paper/2405.10552/) (2024)

## Abstract (arXiv)

Predominately in explainable artificial intelligence (XAI) research, the Shapley value (SV) is applied to determine feature attributions for any black box model. Shapley interaction indices extend the SV to define any-order feature interactions. Defining a unique Shapley interaction index is an open research question and, so far, three definitions have been proposed, which differ by their choice of axioms. Moreover, each definition requires a specific approximation technique. Here, we propose SHAPley Interaction Quantification (SHAP-IQ), an efficient sampling-based approximator to compute Shapley interactions for arbitrary cardinal interaction indices (CII), i.e. interaction indices that satisfy the linearity, symmetry and dummy axiom. SHAP-IQ is based on a novel representation and, in contrast to existing methods, we provide theoretical guarantees for its approximation quality, as well as estimates for the variance of the point estimates. For the special case of SV, our approach reveals a novel representation of the SV and corresponds to Unbiased KernelSHAP with a greatly simplified calculation. We illustrate the computational efficiency and effectiveness by explaining language, image classification and high-dimensional synthetic models.