# Explaining individual predictions when features are dependent: More accurate approximations to Shapley values

arXiv: https://arxiv.org/abs/1903.10464 · HTML: https://mlsanity.com/paper/1903.10464/

## Key facts

- Cited by 208 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Mar 2019.

## Built on by (most cited first, 30 of 208)

- [FastSHAP: Real-Time Shapley Value Estimation](https://mlsanity.com/paper/2107.07436/) (2021)
- [Algorithms to estimate Shapley value feature attributions](https://mlsanity.com/paper/2207.07605/) (2022)
- [Impossibility Theorems for Feature Attribution](https://mlsanity.com/paper/2212.11870/) (2022)
- [Synthetic Benchmarks for Scientific Research in Explainable Machine Learning](https://mlsanity.com/paper/2106.12543/) (2021)
- [Additive MIL: Intrinsically Interpretable Multiple Instance Learning for Pathology](https://mlsanity.com/paper/2206.01794/) (2022)
- [Explaining Black-Box Algorithms Using Probabilistic Contrastive Counterfactuals](https://mlsanity.com/paper/2103.11972/) (2021)
- [Shapley values for feature selection: The good, the bad, and the axioms](https://mlsanity.com/paper/2102.10936/) (2021)
- [Adversarial attacks and defenses in explainable artificial intelligence: A survey](https://mlsanity.com/paper/2306.06123/) (2023)
- [Local Explanations via Necessity and Sufficiency: Unifying Theory and Practice](https://mlsanity.com/paper/2103.14651/) (2021)
- [shapiq: Shapley Interactions for Machine Learning](https://mlsanity.com/paper/2410.01649/) (2024)
- [A Perspective on Explainable Artificial Intelligence Methods: SHAP and LIME](https://mlsanity.com/paper/2305.02012/) (2023)
- [Explaining a Series of Models by Propagating Shapley Values](https://mlsanity.com/paper/2105.00108/) (2021)
- [WeightedSHAP: analyzing and improving Shapley based feature attributions](https://mlsanity.com/paper/2209.13429/) (2022)
- [Explaining Predictive Uncertainty with Information Theoretic Shapley Values](https://mlsanity.com/paper/2306.05724/) (2023)
- [RKHS-SHAP: Shapley Values for Kernel Methods](https://mlsanity.com/paper/2110.09167/) (2021)
- [Interpretable Data-Based Explanations for Fairness Debugging](https://mlsanity.com/paper/2112.09745/) (2021)
- [Fast TreeSHAP: Accelerating SHAP Value Computation for Trees](https://mlsanity.com/paper/2109.09847/) (2021)
- [On Locality of Local Explanation Models](https://mlsanity.com/paper/2106.14648/) (2021)
- [SurvSHAP(t): Time-dependent explanations of machine learning survival models](https://mlsanity.com/paper/2208.11080/) (2022)
- [WindowSHAP: An Efficient Framework for Explaining Time-series Classifiers based on Shapley Values](https://mlsanity.com/paper/2211.06507/) (2022)
- [SHAFF: Fast and consistent SHApley eFfect estimates via random Forests](https://mlsanity.com/paper/2105.11724/) (2021)
- [Counterfactual Shapley Additive Explanations](https://mlsanity.com/paper/2110.14270/) (2021)
- [groupShapley: Efficient prediction explanation with Shapley values for feature groups](https://mlsanity.com/paper/2106.12228/) (2021)
- [Scientific Inference With Interpretable Machine Learning: Analyzing Models to Learn About Real-World Phenomena](https://mlsanity.com/paper/2206.05487/) (2022)
- [Using Shapley Values and Variational Autoencoders to Explain Predictive Models with Dependent Mixed Features](https://mlsanity.com/paper/2111.13507/) (2021)
- [On the Robustness of Removal-Based Feature Attributions](https://mlsanity.com/paper/2306.07462/) (2023)
- [Rational Shapley Values](https://mlsanity.com/paper/2106.10191/) (2021)
- [PredDiff: Explanations and Interactions from Conditional Expectations](https://mlsanity.com/paper/2102.13519/) (2021)
- [Explaining Algorithmic Fairness Through Fairness-Aware Causal Path Decomposition](https://mlsanity.com/paper/2108.05335/) (2021)
- [REPID: Regional Effect Plots with implicit Interaction Detection](https://mlsanity.com/paper/2202.07254/) (2022)

## Abstract (arXiv)

Explaining complex or seemingly simple machine learning models is an important practical problem. We want to explain individual predictions from a complex machine learning model by learning simple, interpretable explanations. Shapley values is a game theoretic concept that can be used for this purpose. The Shapley value framework has a series of desirable theoretical properties, and can in principle handle any predictive model. Kernel SHAP is a computationally efficient approximation to Shapley values in higher dimensions. Like several other existing methods, this approach assumes that the features are independent, which may give very wrong explanations. This is the case even if a simple linear model is used for predictions. In this paper, we extend the Kernel SHAP method to handle dependent features. We provide several examples of linear and non-linear models with various degrees of feature dependence, where our method gives more accurate approximations to the true Shapley values. We also propose a method for aggregating individual Shapley values, such that the prediction can be explained by groups of dependent variables.