# WeightedSHAP: analyzing and improving Shapley based feature attributions

arXiv: https://arxiv.org/abs/2209.13429 · HTML: https://mlsanity.com/paper/2209.13429/

## Key facts

- Cited by 36 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 68 references that are in the map.
- First posted on arXiv 27 Sep 2022.

## Builds on (most cited first, 30 of 35)

- [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)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps](https://mlsanity.com/paper/1312.6034/) (2013)
- [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)
- [Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)](https://mlsanity.com/paper/1511.07289/) (2015)
- [RISE: Randomized Input Sampling for Explanation of Black-box Models](https://mlsanity.com/paper/1806.07421/) (2018)
- [Data Shapley: Equitable Valuation of Data for Machine Learning](https://mlsanity.com/paper/1904.02868/) (2019)
- [The many Shapley values for model explanation](https://mlsanity.com/paper/1908.08474/) (2019)
- [On the Robustness of Interpretability Methods](https://mlsanity.com/paper/1806.08049/) (2018)
- [On the (In)fidelity and Sensitivity for Explanations](https://mlsanity.com/paper/1901.09392/) (2019)
- [Learning to Explain: An Information-Theoretic Perspective on Model Interpretation](https://mlsanity.com/paper/1802.07814/) (2018)
- [Explaining individual predictions when features are dependent: More accurate approximations to Shapley values](https://mlsanity.com/paper/1903.10464/) (2019)
- [Problems with Shapley-value-based explanations as feature importance measures](https://mlsanity.com/paper/2002.11097/) (2020)
- [Feature relevance quantification in explainable AI: A causal problem](https://mlsanity.com/paper/1910.13413/) (2019)
- [Visualizing Deep Neural Network Decisions: Prediction Difference Analysis](https://mlsanity.com/paper/1702.04595/) (2017)
- [Beta Shapley: a Unified and Noise-reduced Data Valuation Framework for Machine Learning](https://mlsanity.com/paper/2110.14049/) (2021)
- [Improving KernelSHAP: Practical Shapley Value Estimation via Linear Regression](https://mlsanity.com/paper/2012.01536/) (2020)
- [Efficient Task-Specific Data Valuation for Nearest Neighbor Algorithms](https://mlsanity.com/paper/1908.08619/) (2019)
- [FastSHAP: Real-Time Shapley Value Estimation](https://mlsanity.com/paper/2107.07436/) (2021)
- [Causal Shapley Values: Exploiting Causal Knowledge to Explain Individual Predictions of Complex Models](https://mlsanity.com/paper/2011.01625/) (2020)
- [Neuron Shapley: Discovering the Responsible Neurons](https://mlsanity.com/paper/2002.09815/) (2020)
- [The Shapley Value in Machine Learning](https://mlsanity.com/paper/2202.05594/) (2022)
- [Shapley explainability on the data manifold](https://mlsanity.com/paper/2006.01272/) (2020)
- [A Distributional Framework for Data Valuation](https://mlsanity.com/paper/2002.12334/) (2020)
- [GTG-Shapley: Efficient and Accurate Participant Contribution Evaluation in Federated Learning](https://mlsanity.com/paper/2109.02053/) (2021)
- [Have We Learned to Explain?: How Interpretability Methods Can Learn to Encode Predictions in their Interpretations](https://mlsanity.com/paper/2103.01890/) (2021)
- [Shapley Flow: A Graph-based Approach to Interpreting Model Predictions](https://mlsanity.com/paper/2010.14592/) (2020)

## Built on by (most cited first, 30 of 36)

- [Data-OOB: Out-of-bag Estimate as a Simple and Efficient Data Value](https://mlsanity.com/paper/2304.07718/) (2023)
- [Stochastic Amortization: A Unified Approach to Accelerate Feature and Data Attribution](https://mlsanity.com/paper/2401.15866/) (2024)
- [Regression-adjusted Monte Carlo Estimators for Shapley Values and Probabilistic Values](https://mlsanity.com/paper/2506.11849/) (2025)
- [To Transformers and Beyond: Large Language Models for the Genome](https://mlsanity.com/paper/2311.07621/) (2023)
- [Stability Guarantees for Feature Attributions with Multiplicative Smoothing](https://mlsanity.com/paper/2307.05902/) (2023)
- [One Sample Fits All: Approximating All Probabilistic Values Simultaneously and Efficiently](https://mlsanity.com/paper/2410.23808/) (2024)
- [Discovering Influential Neuron Path in Vision Transformers](https://mlsanity.com/paper/2503.09046/) (2025)
- [PolySHAP: Extending KernelSHAP with Interaction-Informed Polynomial Regression](https://mlsanity.com/paper/2601.18608/) (2026)
- [A Survey on Contribution Evaluation in Vertical Federated Learning](https://mlsanity.com/paper/2405.02364/) (2024)
- [To Err Is Human: Systematic Quantification of Errors in Published AI Papers via LLM Analysis](https://mlsanity.com/paper/2512.05925/) (2025)
- [A Survey of Explainable AI in Deep Visual Modeling: Methods and Metrics](https://mlsanity.com/paper/2301.13445/) (2023)
- [Efficient Shapley Values Estimation by Amortization for Text Classification](https://mlsanity.com/paper/2305.19998/) (2023)
- [Partial Information Decomposition for Data Interpretability and Feature Selection](https://mlsanity.com/paper/2405.19212/) (2024)
- [CHG Shapley: Efficient Data Valuation and Selection towards Trustworthy Machine Learning](https://mlsanity.com/paper/2406.11730/) (2024)
- [2D-OOB: Attributing Data Contribution Through Joint Valuation Framework](https://mlsanity.com/paper/2408.03572/) (2024)
- [A Unified Framework for Provably Efficient Algorithms to Estimate Shapley Values](https://mlsanity.com/paper/2506.05216/) (2025)
- [TreeGrad-Ranker: Feature Ranking via O(L)-Time Gradients for Decision Trees](https://mlsanity.com/paper/2602.11623/) (2026)
- [TERC: A Transfer Entropy Redundancy Criterion for State Variable Selection in Reinforcement Learning](https://mlsanity.com/paper/2401.11512/) (2024)
- [Looking deeper into interpretable deep learning in neuroimaging: a comprehensive survey](https://mlsanity.com/paper/2307.09615/) (2023)
- [Game-theoretic Counterfactual Explanation for Graph Neural Networks](https://mlsanity.com/paper/2402.06030/) (2024)
- [GARNN: An Interpretable Graph Attentive Recurrent Neural Network for Predicting Blood Glucose Levels via Multivariate Time Series](https://mlsanity.com/paper/2402.16230/) (2024)
- [A Comprehensive Study of Shapley Value in Data Analytics](https://mlsanity.com/paper/2412.01460/) (2024)
- [FW-Shapley: Real-time Estimation of Weighted Shapley Values](https://mlsanity.com/paper/2503.06602/) (2025)
- [Attribution Explanations for Deep Neural Networks: A Theoretical Perspective](https://mlsanity.com/paper/2508.07636/) (2025)
- [Manifold-based Shapley for SAR Recognization Network Explanation](https://mlsanity.com/paper/2401.03128/) (2024)
- [Certified ℓ2 Attribution Robustness via Uniformly Smoothed Attributions](https://mlsanity.com/paper/2405.06361/) (2024)
- [Towards Data Valuation via Asymmetric Data Shapley](https://mlsanity.com/paper/2411.00388/) (2024)
- [Adalina: Adaptive Linear Approximation for the Shapley Value and Beyond](https://mlsanity.com/paper/2604.08438/) (2026)
- [CIMLA: Interpretable AI for inference of differential causal networks](https://mlsanity.com/paper/2304.12523/) (2023)
- [Suboptimal Shapley Value Explanations](https://mlsanity.com/paper/2502.12209/) (2025)

## Abstract (arXiv)

Shapley value is a popular approach for measuring the influence of individual features. While Shapley feature attribution is built upon desiderata from game theory, some of its constraints may be less natural in certain machine learning settings, leading to unintuitive model interpretation. In particular, the Shapley value uses the same weight for all marginal contributions -- i.e. it gives the same importance when a large number of other features are given versus when a small number of other features are given. This property can be problematic if larger feature sets are more or less informative than smaller feature sets. Our work performs a rigorous analysis of the potential limitations of Shapley feature attribution. We identify simple settings where the Shapley value is mathematically suboptimal by assigning larger attributions for less influential features. Motivated by this observation, we propose WeightedSHAP, which generalizes the Shapley value and learns which marginal contributions to focus directly from data. On several real-world datasets, we demonstrate that the influential features identified by WeightedSHAP are better able to recapitulate the model's predictions compared to the features identified by the Shapley value.