# Energy-Based Model for Accurate Estimation of Shapley Values in Feature Attribution

arXiv: https://arxiv.org/abs/2404.01078 · HTML: https://mlsanity.com/paper/2404.01078/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 48 of its 79 references that are in the map.
- First posted on arXiv 1 Apr 2024.

## Builds on (most cited first, 30 of 48)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [Explainable Artificial Intelligence (XAI): Concepts, Taxonomies, Opportunities and Challenges toward Responsible AI](https://mlsanity.com/paper/1910.10045/) (2019)
- [Towards A Rigorous Science of Interpretable Machine Learning](https://mlsanity.com/paper/1702.08608/) (2017)
- [Convolutional Neural Networks for Sentence Classification](https://mlsanity.com/paper/1408.5882/) (2014)
- [Your Classifier is Secretly an Energy Based Model and You Should Treat it Like One](https://mlsanity.com/paper/1912.03263/) (2019)
- [The many Shapley values for model explanation](https://mlsanity.com/paper/1908.08474/) (2019)
- [Explainable Prediction of Medical Codes from Clinical Text](https://mlsanity.com/paper/1802.05695/) (2018)
- [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)
- [Inference Suboptimality in Variational Autoencoders](https://mlsanity.com/paper/1801.03558/) (2018)
- [FastSHAP: Real-Time Shapley Value Estimation](https://mlsanity.com/paper/2107.07436/) (2021)
- [XRAI: Better Attributions Through Regions](https://mlsanity.com/paper/1906.02825/) (2019)
- [Explaining Deep Neural Networks with a Polynomial Time Algorithm for Shapley Values Approximation](https://mlsanity.com/paper/1903.10992/) (2019)
- [Algorithms to estimate Shapley value feature attributions](https://mlsanity.com/paper/2207.07605/) (2022)
- [Deep Structured Energy Based Models for Anomaly Detection](https://mlsanity.com/paper/1605.07717/) (2016)
- [ICE-BeeM: Identifiable Conditional Energy-Based Deep Models Based on Nonlinear ICA](https://mlsanity.com/paper/2002.11537/) (2020)
- [Sampling Permutations for Shapley Value Estimation](https://mlsanity.com/paper/2104.12199/) (2021)
- [L-Shapley and C-Shapley: Efficient Model Interpretation for Structured Data](https://mlsanity.com/paper/1808.02610/) (2018)
- [Deep Learning for Financial Applications : A Survey](https://mlsanity.com/paper/2002.05786/) (2020)
- [Explaining the Explainer: A First Theoretical Analysis of LIME](https://mlsanity.com/paper/2001.03447/) (2020)
- [Shapley explainability on the data manifold](https://mlsanity.com/paper/2006.01272/) (2020)
- [Generalized Energy Based Models](https://mlsanity.com/paper/2003.05033/) (2020)
- [Faith-Shap: The Faithful Shapley Interaction Index](https://mlsanity.com/paper/2203.00870/) (2022)
- [Efficient nonparametric statistical inference on population feature importance using Shapley values](https://mlsanity.com/paper/2006.09481/) (2020)
- [From Shapley Values to Generalized Additive Models and back](https://mlsanity.com/paper/2209.04012/) (2022)
- [Shapley values for feature selection: The good, the bad, and the axioms](https://mlsanity.com/paper/2102.10936/) (2021)
- [SHAP-IQ: Unified Approximation of any-order Shapley Interactions](https://mlsanity.com/paper/2303.01179/) (2023)

## Built on by (most cited first, 1 of 1)

- [SIM-Shapley: A Stable and Computationally Efficient Approach to Shapley Value Approximation](https://mlsanity.com/paper/2505.08198/) (2025)

## Abstract (arXiv)

Shapley value is a widely used tool in explainable artificial intelligence (XAI), as it provides a principled way to attribute contributions of input features to model outputs. However, estimation of Shapley value requires capturing conditional dependencies among all feature combinations, which poses significant challenges in complex data environments. In this article, EmSHAP (Energy-based model for Shapley value estimation), an accurate Shapley value estimation method, is proposed to estimate the expectation of Shapley contribution function under the arbitrary subset of features given the rest. By utilizing the ability of energy-based model (EBM) to model complex distributions, EmSHAP provides an effective solution for estimating the required conditional probabilities. To further improve estimation accuracy, a GRU (Gated Recurrent Unit)-coupled partition function estimation method is introduced. The GRU network captures long-term dependencies with a lightweight parameterization and maps input features into a latent space to mitigate the influence of feature ordering. Additionally, a dynamic masking mechanism is incorporated to further enhance the robustness and accuracy by progressively increasing the masking rate. Theoretical analysis on the error bound as well as application to four case studies verified the higher accuracy and better scalability of EmSHAP in contrast to competitive methods.