# SVARM-IQ: Efficient Approximation of Any-order Shapley Interactions through Stratification

arXiv: https://arxiv.org/abs/2401.13371 · HTML: https://mlsanity.com/paper/2401.13371/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Jan 2024.

## Built on by (most cited first, 16 of 16)

- [shapiq: Shapley Interactions for Machine Learning](https://mlsanity.com/paper/2410.01649/) (2024)
- [KernelSHAP-IQ: Weighted Least-Square Optimization for Shapley Interactions](https://mlsanity.com/paper/2405.10852/) (2024)
- [ProxySPEX: Inference-Efficient Interpretability via Sparse Feature Interactions in LLMs](https://mlsanity.com/paper/2505.17495/) (2025)
- [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)
- [Exactly Computing do-Shapley Values](https://mlsanity.com/paper/2602.07203/) (2026)
- [Energy-Based Model for Accurate Estimation of Shapley Values in Feature Attribution](https://mlsanity.com/paper/2404.01078/) (2024)
- [Interaction Tensor SHAP](https://mlsanity.com/paper/2512.05338/) (2025)
- [Functional Decomposition and Shapley Interactions for Interpreting Survival Models](https://mlsanity.com/paper/2602.16505/) (2026)
- [OrdShap: Feature Position Importance for Sequential Black-Box Models](https://mlsanity.com/paper/2507.11855/) (2025)
- [CUBE: Contrastive Understanding by Balanced Experiments](https://mlsanity.com/paper/2509.10825/) (2025)
- [TT-FSI: Scalable Faithful Shapley Interactions via Tensor-Train](https://mlsanity.com/paper/2601.01903/) (2026)
- [ConfoundingSHAP: Quantifying confounding strength in causal inference](https://mlsanity.com/paper/2605.10533/) (2026)
- [Verified SHAP: Provable Bounds for Exact Shapley Values of Neural Networks](https://mlsanity.com/paper/2605.24084/) (2026)
- [OperatorSHAP: Fast and Accurate Shapley Value Estimation for Neural Operators](https://mlsanity.com/paper/2606.28065/) (2026)

## Abstract (arXiv)

Addressing the limitations of individual attribution scores via the Shapley value (SV), the field of explainable AI (XAI) has recently explored intricate interactions of features or data points. In particular, extensions of the SV, such as the Shapley Interaction Index (SII), have been proposed as a measure to still benefit from the axiomatic basis of the SV. However, similar to the SV, their exact computation remains computationally prohibitive. Hence, we propose with SVARM-IQ a sampling-based approach to efficiently approximate Shapley-based interaction indices of any order. SVARM-IQ can be applied to a broad class of interaction indices, including the SII, by leveraging a novel stratified representation. We provide non-asymptotic theoretical guarantees on its approximation quality and empirically demonstrate that SVARM-IQ achieves state-of-the-art estimation results in practical XAI scenarios on different model classes and application domains.