# Fast Hierarchical Games for Image Explanations

arXiv: https://arxiv.org/abs/2104.06164 · HTML: https://mlsanity.com/paper/2104.06164/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 50 references that are in the map.
- First posted on arXiv 13 Apr 2021.

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

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [Learning Important Features Through Propagating Activation Differences](https://mlsanity.com/paper/1704.02685/) (2017)
- [Sanity Checks for Saliency Maps](https://mlsanity.com/paper/1810.03292/) (2018)
- [The many Shapley values for model explanation](https://mlsanity.com/paper/1908.08474/) (2019)
- [Explaining by Removing: A Unified Framework for Model Explanation](https://mlsanity.com/paper/2011.14878/) (2020)
- [Explaining individual predictions when features are dependent: More accurate approximations to Shapley values](https://mlsanity.com/paper/1903.10464/) (2019)
- [Feature relevance quantification in explainable AI: A causal problem](https://mlsanity.com/paper/1910.13413/) (2019)
- [True to the Model or True to the Data?](https://mlsanity.com/paper/2006.16234/) (2020)
- [Asymmetric Shapley values: incorporating causal knowledge into model-agnostic explainability](https://mlsanity.com/paper/1910.06358/) (2019)
- [L-Shapley and C-Shapley: Efficient Model Interpretation for Structured Data](https://mlsanity.com/paper/1808.02610/) (2018)
- [Multi-scale Domain-adversarial Multiple-instance CNN for Cancer Subtype Classification with Unannotated Histopathological Images](https://mlsanity.com/paper/2001.01599/) (2020)
- [Hierarchical interpretations for neural network predictions](https://mlsanity.com/paper/1806.05337/) (2018)
- [Generating Hierarchical Explanations on Text Classification via Feature Interaction Detection](https://mlsanity.com/paper/2004.02015/) (2020)
- [Do Input Gradients Highlight Discriminative Features?](https://mlsanity.com/paper/2102.12781/) (2021)
- [Interpretable to Whom? A Role-based Model for Analyzing Interpretable Machine Learning Systems](https://mlsanity.com/paper/1806.07552/) (2018)
- [Explaining Models by Propagating Shapley Values of Local Components](https://mlsanity.com/paper/1911.11888/) (2019)
- [On Baselines for Local Feature Attributions](https://mlsanity.com/paper/2101.00905/) (2021)
- [A Rate-Distortion Framework for Explaining Neural Network Decisions](https://mlsanity.com/paper/1905.11092/) (2019)
- [In-Distribution Interpretability for Challenging Modalities](https://mlsanity.com/paper/2007.00758/) (2020)

## Built on by (most cited first, 15 of 15)

- [Data Banzhaf: A Robust Data Valuation Framework for Machine Learning](https://mlsanity.com/paper/2205.15466/) (2022)
- [SHAP-XRT: The Shapley Value Meets Conditional Independence Testing](https://mlsanity.com/paper/2207.07038/) (2022)
- [Approximating Score-based Explanation Techniques Using Conformal Regression](https://mlsanity.com/paper/2308.11975/) (2023)
- [I Bet You Did Not Mean That: Testing Semantic Importance via Betting](https://mlsanity.com/paper/2405.19146/) (2024)
- [Sufficient and Necessary Explanations (and What Lies in Between)](https://mlsanity.com/paper/2409.20427/) (2024)
- [Prediction via Shapley Value Regression](https://mlsanity.com/paper/2505.04775/) (2025)
- [Interpreting Vision and Language Generative Models with Semantic Visual Priors](https://mlsanity.com/paper/2304.14986/) (2023)
- [Fast Shapley Value Estimation: A Unified Approach](https://mlsanity.com/paper/2311.01010/) (2023)
- [ShapBPT: Image Feature Attributions Using Data-Aware Binary Partition Trees](https://mlsanity.com/paper/2602.07047/) (2026)
- [MarkerMap: nonlinear marker selection for single-cell studies](https://mlsanity.com/paper/2207.14106/) (2022)
- [Weakly Supervised Learning Significantly Reduces the Number of Labels Required for Intracranial Hemorrhage Detection on Head CT](https://mlsanity.com/paper/2211.15924/) (2022)
- [Direct Preference Optimization for Adaptive Concept-based Explanations](https://mlsanity.com/paper/2505.15626/) (2025)
- [Desensitizing for Improving Corruption Robustness in Point Cloud Classification through Adversarial Training](https://mlsanity.com/paper/2509.23010/) (2025)
- [Owen-based Semantics and Hierarchy-Aware Explanation (O-Shap)](https://mlsanity.com/paper/2602.17107/) (2026)
- [MorphoSHAP: Rethinking the Unit of Attribution in Explanation for Deep Visual Models](https://mlsanity.com/paper/2609.25815/) (2026)

## Abstract (arXiv)

As modern complex neural networks keep breaking records and solving harder problems, their predictions also become less and less intelligible. The current lack of interpretability often undermines the deployment of accurate machine learning tools in sensitive settings. In this work, we present a model-agnostic explanation method for image classification based on a hierarchical extension of Shapley coefficients--Hierarchical Shap (h-Shap)--that resolves some of the limitations of current approaches. Unlike other Shapley-based explanation methods, h-Shap is scalable and can be computed without the need of approximation. Under certain distributional assumptions, such as those common in multiple instance learning, h-Shap retrieves the exact Shapley coefficients with an exponential improvement in computational complexity. We compare our hierarchical approach with popular Shapley-based and non-Shapley-based methods on a synthetic dataset, a medical imaging scenario, and a general computer vision problem, showing that h-Shap outperforms the state of the art in both accuracy and runtime. Code and experiments are made publicly available.