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shapiq: Shapley Interactions for Machine Learning
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Introduces shapiq, an open-source Python package unifying algorithms for computing Shapley values and any-order Shapley interactions, plus a benchmark suite of 100 games (2,042 pre-computed configurations) across ML domains.
Problem
Computing Shapley values and Shapley interactions exactly is exponential in the number of players, and existing tools (e.g., shap) offer few approximators limited to first-order feature attributions, with no common benchmark for higher-order interaction approximators.
Approach
A unified, application-agnostic library of exact computers, approximators (for SV and k-SII, STII, FSII), and explainers (TabularExplainer, TreeExplainer with TreeSHAP-IQ), coupled with pre-computed ground-truth games across 11 ML benchmark applications for systematic comparison.
Key results
- Pairwise k-SII substantially improves Shapley-weighted R^2 over SV (SHAP) across ML applications, and higher explanation orders yield more faithful explanations.
- Best-performing approximator varies by domain: kernel-based methods (KernelSHAP variants) lead on Local Explanation and Uncertainty Explanation, while stratification-based SVARM/SVARM-IQ lead on Data Valuation, Dataset Valuation, and Ensemble Selection.
- The library computes 18 interaction indices and game-theoretic concepts and provides pre-computed ground truth for 2,042 benchmark game configurations.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Increase explanation order from feature attributions to pairwise Shapley interactions | Shapley interactions · Synthetic and real-world ML applications | Shapley-weighted faithfulness | Helped |
| Increase explanation order | Shapley interactions · Synthetic and real-world ML applications | Shapley-weighted faithfulness | Helped |
| Use a larger explanation order when higher-order interactions dominate | Shapley interactions · Games dominated by higher-order interactions | Shapley-weighted faithfulness | Helped |
| Use FSII instead of other interaction indices | Shapley interactions · Shapley-weighted faithfulness evaluation | Shapley-weighted faithfulness | Helped |
| Increase interaction size | Shapley interactions · Synthetic single-interaction games | Shapley-weighted faithfulness | Hurt |
| Use kernel-based estimators | Shapley-value and Shapley-interaction approximation methods · Local Explanation, Uncertainty Explanation, and Unsupervised Feature Importance | MSE | Helped |
| Use stratification-based estimators | Shapley-value and Shapley-interaction approximation methods · Data Valuation, Dataset Valuation, and Ensemble Selection | MSE | Helped |
| Use mean-estimation methods instead of the leading kernel- or stratification-based estimators | Shapley-value and Shapley-interaction approximation methods · Across benchmark applications | MSE | Hurt |
| Use stratification-based rather than kernel-based estimators | Shapley-value and Shapley-interaction approximation methods · Games where coalition size naturally impacts worth, including Dataset Valuation | MSE | Helped |
| Use kernel-based rather than stratification-based estimators | Shapley-value and Shapley-interaction approximation methods · Games where coalition-size and worth dependency is less pronounced, including Local Explanation | MSE | Helped |
| Approximate games dominated by higher-order interactions with kernel-based estimators | Kernel-based estimators · Games with higher-order interactions | Approximation accuracy | Hurt |
Surprising findings
- Kernel-based approximators degrade when higher-order interactions dominate the game's Möbius structure, whereas stratified methods remain strong in such settings.
Limitations
- TreeSHAP-IQ is implemented only in Python, whereas a C++ implementation could be more efficient.
- Shapley interactions can be misinterpreted when the wrong index is chosen for the application.
- Visualizing higher-order interactions is challenging and may cause information overload; human-centric evaluation is needed.
Experimental setup
Datasets: AdultCensus BikeSharing CaliforniaHousing MovieReview (IMDB) ImageNet OpenML
Benchmarks: shapiq benchmark games (11 applications)
Metrics: MSE precision Shapley-weighted R^2
Baselines: KernelSHAP SVARM Permutation Sampling Owen Sampling Stratified Sampling Unbiased KernelSHAP k-ADD-SHAP
Builds on: SHAP TreeSHAP KernelSHAP SHAP-IQ SVARM TreeSHAP-IQ
Closest papers by meaning
- KernelSHAP-IQ: Weighted Least Square Optimization for Shapley Interactions (ICML 2024 · similarity 0.92)
- Beyond TreeSHAP: Efficient Computation of Any-Order Shapley Interactions for Tree Ensembles (AAAI 2024 · similarity 0.89)
- Provably Accurate Shapley Value Estimation via Leverage Score Sampling (ICLR 2025 · similarity 0.89)
- Unlocking the Game: Estimating Games in Möbius Representation for Explanation and High-Order Interaction Detection (AAAI 2025 · similarity 0.89)
- A Unified Framework for Provably Efficient Algorithms to Estimate Shapley Values (NeurIPS 2025 · similarity 0.88)
- Support Vector-based Estimation of Multilinear Games for Feature Selection and Explanation (AAAI 2025 · similarity 0.88)
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