# A Comparative Study of Methods for Estimating Conditional Shapley Values and When to Use Them

arXiv: https://arxiv.org/abs/2305.09536 · HTML: https://mlsanity.com/paper/2305.09536/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 44 of its 122 references that are in the map.
- First posted on arXiv 16 May 2023.

## Builds on (most cited first, 30 of 44)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [An Introduction to Variational Autoencoders](https://mlsanity.com/paper/1906.02691/) (2019)
- [GAIN: Missing Data Imputation using Generative Adversarial Nets](https://mlsanity.com/paper/1806.02920/) (2018)
- [The many Shapley values for model explanation](https://mlsanity.com/paper/1908.08474/) (2019)
- [Consistent Individualized Feature Attribution for Tree Ensembles](https://mlsanity.com/paper/1802.03888/) (2018)
- [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)
- [Problems with Shapley-value-based explanations as feature importance measures](https://mlsanity.com/paper/2002.11097/) (2020)
- [ranger: A Fast Implementation of Random Forests for High Dimensional Data in C++ and R](https://mlsanity.com/paper/1508.04409/) (2015)
- [True to the Model or True to the Data?](https://mlsanity.com/paper/2006.16234/) (2020)
- [FastSHAP: Real-Time Shapley Value Estimation](https://mlsanity.com/paper/2107.07436/) (2021)
- [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)
- [Causal Shapley Values: Exploiting Causal Knowledge to Explain Individual Predictions of Complex Models](https://mlsanity.com/paper/2011.01625/) (2020)
- [Sampling Permutations for Shapley Value Estimation](https://mlsanity.com/paper/2104.12199/) (2021)
- [Neural Autoregressive Distribution Estimation](https://mlsanity.com/paper/1605.02226/) (2016)
- [Shapley explainability on the data manifold](https://mlsanity.com/paper/2006.01272/) (2020)
- [Entity Embeddings of Categorical Variables](https://mlsanity.com/paper/1604.06737/) (2016)
- [Diffusion models for missing value imputation in tabular data](https://mlsanity.com/paper/2210.17128/) (2022)
- [TimeSHAP: Explaining Recurrent Models through Sequence Perturbations](https://mlsanity.com/paper/2012.00073/) (2020)
- [Variational Autoencoder with Arbitrary Conditioning](https://mlsanity.com/paper/1806.02382/) (2018)
- [GraphSVX: Shapley Value Explanations for Graph Neural Networks](https://mlsanity.com/paper/2104.10482/) (2021)
- [Efficient nonparametric statistical inference on population feature importance using Shapley values](https://mlsanity.com/paper/2006.09481/) (2020)
- [Shapley values for feature selection: The good, the bad, and the axioms](https://mlsanity.com/paper/2102.10936/) (2021)
- [Shapley Flow: A Graph-based Approach to Interpreting Model Predictions](https://mlsanity.com/paper/2010.14592/) (2020)
- [Explaining a Series of Models by Propagating Shapley Values](https://mlsanity.com/paper/2105.00108/) (2021)
- [A Multilinear Sampling Algorithm to Estimate Shapley Values](https://mlsanity.com/paper/2010.12082/) (2020)

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

- [shapiq: Shapley Interactions for Machine Learning](https://mlsanity.com/paper/2410.01649/) (2024)
- [Explaining Predictive Uncertainty with Information Theoretic Shapley Values](https://mlsanity.com/paper/2306.05724/) (2023)
- [Unifying Feature-Based Explanations with Functional ANOVA and Cooperative Game Theory](https://mlsanity.com/paper/2412.17152/) (2024)
- [PolySHAP: Extending KernelSHAP with Interaction-Informed Polynomial Regression](https://mlsanity.com/paper/2601.18608/) (2026)
- [Improving the Weighting Strategy in KernelSHAP](https://mlsanity.com/paper/2410.04883/) (2024)
- [shapr: Explaining Machine Learning Models with Conditional Shapley Values in R and Python](https://mlsanity.com/paper/2504.01842/) (2025)
- [Interpretable Machine Learning for Survival Analysis](https://mlsanity.com/paper/2403.10250/) (2024)
- [Efficient and Accurate Explanation Estimation with Distribution Compression](https://mlsanity.com/paper/2406.18334/) (2024)
- [A Comprehensive Study of Shapley Value in Data Analytics](https://mlsanity.com/paper/2412.01460/) (2024)
- [Precision of Individual Shapley Value Explanations](https://mlsanity.com/paper/2312.03485/) (2023)
- [Computing Conditional Shapley Values Using Tabular Foundation Models](https://mlsanity.com/paper/2602.09489/) (2026)
- [Notes on Applicability of Explainable AI Methods to Machine Learning Models Using Features Extracted by Persistent Homology](https://mlsanity.com/paper/2310.09780/) (2023)
- [From Abstract to Actionable: Pairwise Shapley Values for Explainable AI](https://mlsanity.com/paper/2502.12525/) (2025)
- [Fast approximate estimation of conditional Shapley values when using a linear explainer](https://mlsanity.com/paper/2504.18167/) (2025)
- [How important are the genes to explain the outcome - the asymmetric Shapley value as an honest importance metric for high-dimensional features](https://mlsanity.com/paper/2603.05317/) (2026)

## Abstract (arXiv)

Shapley values originated in cooperative game theory but are extensively used today as a model-agnostic explanation framework to explain predictions made by complex machine learning models in the industry and academia. There are several algorithmic approaches for computing different versions of Shapley value explanations. Here, we focus on conditional Shapley values for predictive models fitted to tabular data. Estimating precise conditional Shapley values is difficult as they require the estimation of non-trivial conditional expectations. In this article, we develop new methods, extend earlier proposed approaches, and systematize the new refined and existing methods into different method classes for comparison and evaluation. The method classes use either Monte Carlo integration or regression to model the conditional expectations. We conduct extensive simulation studies to evaluate how precisely the different method classes estimate the conditional expectations, and thereby the conditional Shapley values, for different setups. We also apply the methods to several real-world data experiments and provide recommendations for when to use the different method classes and approaches. Roughly speaking, we recommend using parametric methods when we can specify the data distribution almost correctly, as they generally produce the most accurate Shapley value explanations. When the distribution is unknown, both generative methods and regression models with a similar form as the underlying predictive model are good and stable options. Regression-based methods are often slow to train but produce the Shapley value explanations quickly once trained. The vice versa is true for Monte Carlo-based methods, making the different methods appropriate in different practical situations.