# Using Shapley Values and Variational Autoencoders to Explain Predictive Models with Dependent Mixed Features

arXiv: https://arxiv.org/abs/2111.13507 · HTML: https://mlsanity.com/paper/2111.13507/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 95 references that are in the map.
- First posted on arXiv 26 Nov 2021.

## Builds on (most cited first, 30 of 37)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Analyzing and Improving the Image Quality of StyleGAN](https://mlsanity.com/paper/1912.04958/) (2019)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Visualizing the Loss Landscape of Neural Nets](https://mlsanity.com/paper/1712.09913/) (2017)
- [An Introduction to Variational Autoencoders](https://mlsanity.com/paper/1906.02691/) (2019)
- [Deep Neural Networks are Easily Fooled: High Confidence Predictions for Unrecognizable Images](https://mlsanity.com/paper/1412.1897/) (2014)
- [Generating Sentences from a Continuous Space](https://mlsanity.com/paper/1511.06349/) (2015)
- [GAIN: Missing Data Imputation using Generative Adversarial Nets](https://mlsanity.com/paper/1806.02920/) (2018)
- [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)
- [ranger: A Fast Implementation of Random Forests for High Dimensional Data in C++ and R](https://mlsanity.com/paper/1508.04409/) (2015)
- [A Hierarchical Latent Vector Model for Learning Long-Term Structure in Music](https://mlsanity.com/paper/1803.05428/) (2018)
- [True to the Model or True to the Data?](https://mlsanity.com/paper/2006.16234/) (2020)
- [Asymmetric Shapley values: incorporating causal knowledge into model-agnostic explainability](https://mlsanity.com/paper/1910.06358/) (2019)
- [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)
- [Shapley explainability on the data manifold](https://mlsanity.com/paper/2006.01272/) (2020)
- [Variational Autoencoder with Arbitrary Conditioning](https://mlsanity.com/paper/1806.02382/) (2018)
- [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)
- [groupShapley: Efficient prediction explanation with Shapley values for feature groups](https://mlsanity.com/paper/2106.12228/) (2021)
- [Explaining predictive models with mixed features using Shapley values and conditional inference trees](https://mlsanity.com/paper/2007.01027/) (2020)
- [CosmoGAN: creating high-fidelity weak lensing convergence maps using Generative Adversarial Networks](https://mlsanity.com/paper/1706.02390/) (2017)

## Built on by (most cited first, 19 of 19)

- [Algorithms to estimate Shapley value feature attributions](https://mlsanity.com/paper/2207.07605/) (2022)
- [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)
- [Decoupling Pixel Flipping and Occlusion Strategy for Consistent XAI Benchmarks](https://mlsanity.com/paper/2401.06654/) (2024)
- [SurvSHAP(t): Time-dependent explanations of machine learning survival models](https://mlsanity.com/paper/2208.11080/) (2022)
- [A Comparative Study of Methods for Estimating Conditional Shapley Values and When to Use Them](https://mlsanity.com/paper/2305.09536/) (2023)
- [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)
- [Approximation of group explainers with coalition structure using Monte Carlo sampling on the product space of coalitions and features](https://mlsanity.com/paper/2303.10216/) (2023)
- [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)
- [Energy-Based Model for Accurate Estimation of Shapley Values in Feature Attribution](https://mlsanity.com/paper/2404.01078/) (2024)
- [Interaction Tensor SHAP](https://mlsanity.com/paper/2512.05338/) (2025)
- [Computing Conditional Shapley Values Using Tabular Foundation Models](https://mlsanity.com/paper/2602.09489/) (2026)
- [Functional Decomposition and Shapley Interactions for Interpreting Survival Models](https://mlsanity.com/paper/2602.16505/) (2026)
- [Explain Variance of Prediction in Variational Time Series Models for Clinical Deterioration Prediction](https://mlsanity.com/paper/2402.06808/) (2024)
- [On the influence of dependent features in classification problems: a game-theoretic perspective](https://mlsanity.com/paper/2408.02481/) (2024)

## Abstract (arXiv)

Shapley values are today extensively used as a model-agnostic explanation framework to explain complex predictive machine learning models. Shapley values have desirable theoretical properties and a sound mathematical foundation in the field of cooperative game theory. Precise Shapley value estimates for dependent data rely on accurate modeling of the dependencies between all feature combinations. In this paper, we use a variational autoencoder with arbitrary conditioning (VAEAC) to model all feature dependencies simultaneously. We demonstrate through comprehensive simulation studies that our VAEAC approach to Shapley value estimation outperforms the state-of-the-art methods for a wide range of settings for both continuous and mixed dependent features. For high-dimensional settings, our VAEAC approach with a non-uniform masking scheme significantly outperforms competing methods. Finally, we apply our VAEAC approach to estimate Shapley value explanations for the Abalone data set from the UCI Machine Learning Repository.