# KernelSHAP-IQ: Weighted Least-Square Optimization for Shapley Interactions

arXiv: https://arxiv.org/abs/2405.10852 · HTML: https://mlsanity.com/paper/2405.10852/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 65 references that are in the map.
- First posted on arXiv 17 May 2024.

## Builds on (most cited first, 30 of 31)

- [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)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [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)
- [Fooling LIME and SHAP: Adversarial Attacks on Post hoc Explanation Methods](https://mlsanity.com/paper/1911.02508/) (2019)
- [Explaining by Removing: A Unified Framework for Model Explanation](https://mlsanity.com/paper/2011.14878/) (2020)
- [Problems with Shapley-value-based explanations as feature importance measures](https://mlsanity.com/paper/2002.11097/) (2020)
- [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)
- [FastSHAP: Real-Time Shapley Value Estimation](https://mlsanity.com/paper/2107.07436/) (2021)
- [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)
- [OpenML-Python: an extensible Python API for OpenML](https://mlsanity.com/paper/1911.02490/) (2019)
- [From Shapley Values to Generalized Additive Models and back](https://mlsanity.com/paper/2209.04012/) (2022)
- [SHAP-IQ: Unified Approximation of any-order Shapley Interactions](https://mlsanity.com/paper/2303.01179/) (2023)
- [Purifying Interaction Effects with the Functional ANOVA: An Efficient Algorithm for Recovering Identifiable Additive Models](https://mlsanity.com/paper/1911.04974/) (2019)
- [Approximating the Shapley Value without Marginal Contributions](https://mlsanity.com/paper/2302.00736/) (2023)
- [Feature Interaction Interpretability: A Case for Explaining Ad-Recommendation Systems via Neural Interaction Detection](https://mlsanity.com/paper/2006.10966/) (2020)
- [Beyond TreeSHAP: Efficient Computation of Any-Order Shapley Interactions for Tree Ensembles](https://mlsanity.com/paper/2401.12069/) (2024)
- [Unifying local and global model explanations by functional decomposition of low dimensional structures](https://mlsanity.com/paper/2208.06151/) (2022)
- [Decomposing Global Feature Effects Based on Feature Interactions](https://mlsanity.com/paper/2306.00541/) (2023)
- [SVARM-IQ: Efficient Approximation of Any-order Shapley Interactions through Stratification](https://mlsanity.com/paper/2401.13371/) (2024)
- [Joint Shapley values: a measure of joint feature importance](https://mlsanity.com/paper/2107.11357/) (2021)
- [Statistical Aspects of SHAP: Functional ANOVA for Model Interpretation](https://mlsanity.com/paper/2208.09970/) (2022)

## Built on by (most cited first, 22 of 22)

- [shapiq: Shapley Interactions for Machine Learning](https://mlsanity.com/paper/2410.01649/) (2024)
- [Unifying Feature-Based Explanations with Functional ANOVA and Cooperative Game Theory](https://mlsanity.com/paper/2412.17152/) (2024)
- [SHAP Meets Tensor Networks: Provably Tractable Explanations with Parallelism](https://mlsanity.com/paper/2510.21599/) (2025)
- [Explaining Similarity in Vision-Language Encoders with Weighted Banzhaf Interactions](https://mlsanity.com/paper/2508.05430/) (2025)
- [Improving the Weighting Strategy in KernelSHAP](https://mlsanity.com/paper/2410.04883/) (2024)
- [Disentangling Interactions and Dependencies in Feature Attribution](https://mlsanity.com/paper/2410.23772/) (2024)
- [HyperSHAP: Shapley Values and Interactions for Explaining Hyperparameter Optimization](https://mlsanity.com/paper/2502.01276/) (2025)
- [A Unified Framework for Provably Efficient Algorithms to Estimate Shapley Values](https://mlsanity.com/paper/2506.05216/) (2025)
- [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)
- [Tractable Shapley Values and Interactions via Tensor Networks](https://mlsanity.com/paper/2510.22138/) (2025)
- [Order-Level Attention Similarity Across Language Models: A Latent Commonality](https://mlsanity.com/paper/2511.05064/) (2025)
- [Surrogate Modeling for Explainable Predictive Time Series Corrections](https://mlsanity.com/paper/2412.19897/) (2024)
- [SIM-Shapley: A Stable and Computationally Efficient Approach to Shapley Value Approximation](https://mlsanity.com/paper/2505.08198/) (2025)
- [Functional Decomposition and Shapley Interactions for Interpreting Survival Models](https://mlsanity.com/paper/2602.16505/) (2026)
- [The Representational Limit of Scalar Interactions: An Interventional Decomposition](https://mlsanity.com/paper/2606.19410/) (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)
- [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)

The Shapley value (SV) is a prevalent approach of allocating credit to machine learning (ML) entities to understand black box ML models. Enriching such interpretations with higher-order interactions is inevitable for complex systems, where the Shapley Interaction Index (SII) is a direct axiomatic extension of the SV. While it is well-known that the SV yields an optimal approximation of any game via a weighted least square (WLS) objective, an extension of this result to SII has been a long-standing open problem, which even led to the proposal of an alternative index. In this work, we characterize higher-order SII as a solution to a WLS problem, which constructs an optimal approximation via SII and k-Shapley values (k-SII). We prove this representation for the SV and pairwise SII and give empirically validated conjectures for higher orders. As a result, we propose KernelSHAP-IQ, a direct extension of KernelSHAP for SII, and demonstrate state-of-the-art performance for feature interactions.