# FW-Shapley: Real-time Estimation of Weighted Shapley Values

arXiv: https://arxiv.org/abs/2503.06602 · HTML: https://mlsanity.com/paper/2503.06602/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 38 references that are in the map.
- First posted on arXiv 9 Mar 2025.

## Builds on (most cited first, 25 of 25)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [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)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (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)
- [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)
- [Captum: A unified and generic model interpretability library for PyTorch](https://mlsanity.com/paper/2009.07896/) (2020)
- [A Benchmark for Interpretability Methods in Deep Neural Networks](https://mlsanity.com/paper/1806.10758/) (2018)
- [Explaining by Removing: A Unified Framework for Model Explanation](https://mlsanity.com/paper/2011.14878/) (2020)
- [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)
- [Explaining Deep Neural Networks with a Polynomial Time Algorithm for Shapley Values Approximation](https://mlsanity.com/paper/1903.10992/) (2019)
- [L-Shapley and C-Shapley: Efficient Model Interpretation for Structured Data](https://mlsanity.com/paper/1808.02610/) (2018)
- [Neuron Shapley: Discovering the Responsible Neurons](https://mlsanity.com/paper/2002.09815/) (2020)
- [Shapley explainability on the data manifold](https://mlsanity.com/paper/2006.01272/) (2020)
- [Have We Learned to Explain?: How Interpretability Methods Can Learn to Encode Predictions in their Interpretations](https://mlsanity.com/paper/2103.01890/) (2021)
- [Learning to Estimate Shapley Values with Vision Transformers](https://mlsanity.com/paper/2206.05282/) (2022)
- [Efficient computation and analysis of distributional Shapley values](https://mlsanity.com/paper/2007.01357/) (2020)
- [WeightedSHAP: analyzing and improving Shapley based feature attributions](https://mlsanity.com/paper/2209.13429/) (2022)
- [The Shapley Value of Classifiers in Ensemble Games](https://mlsanity.com/paper/2101.02153/) (2021)
- [Efficient Computation of the Shapley Value for Game-Theoretic Network Centrality](https://mlsanity.com/paper/1402.0567/) (2014)

## Built on by (most cited first, 2 of 2)

- [Losing is for Cherishing: Data Valuation Based on Machine Unlearning and Shapley Value](https://mlsanity.com/paper/2505.16147/) (2025)
- [An Enhanced Focal Loss Function to Mitigate Class Imbalance in Auto Insurance Fraud Detection with Explainable AI](https://mlsanity.com/paper/2508.02283/) (2025)

## Abstract (arXiv)

Fair credit assignment is essential in various machine learning (ML) applications, and Shapley values have emerged as a valuable tool for this purpose. However, in critical ML applications such as data valuation and feature attribution, the uniform weighting of Shapley values across subset cardinalities leads to unintuitive credit assignments. To address this, weighted Shapley values were proposed as a generalization, allowing different weights for subsets with different cardinalities. Despite their advantages, similar to Shapley values, Weighted Shapley values suffer from exponential compute costs, making them impractical for high-dimensional datasets. To tackle this issue, we present two key contributions. Firstly, we provide a weighted least squares characterization of weighted Shapley values. Next, using this characterization, we propose Fast Weighted Shapley (FW-Shapley), an amortized framework for efficiently computing weighted Shapley values using a learned estimator. We further show that our estimator's training procedure is theoretically valid even though we do not use ground truth Weighted Shapley values during training. On the feature attribution task, we outperform the learned estimator FastSHAP by 27% (on average) in terms of Inclusion AUC. For data valuation, we are much faster (14 times) while being comparable to the state-of-the-art KNN Shapley.