# Explaining predictive models using Shapley values and non-parametric vine copulas

arXiv: https://arxiv.org/abs/2102.06416 · HTML: https://mlsanity.com/paper/2102.06416/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 41 references that are in the map.
- First posted on arXiv 12 Feb 2021.

## Builds on (most cited first, 9 of 9)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [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)
- [True to the Model or True to the Data?](https://mlsanity.com/paper/2006.16234/) (2020)
- [Converting High-Dimensional Regression to High-Dimensional Conditional Density Estimation](https://mlsanity.com/paper/1704.08095/) (2017)
- [Evading the curse of dimensionality in nonparametric density estimation with simplified vine copulas](https://mlsanity.com/paper/1503.03305/) (2015)
- [Prediction based on conditional distributions of vine copulas](https://mlsanity.com/paper/1807.08429/) (2018)
- [Solving estimating equations with copulas](https://mlsanity.com/paper/1801.10576/) (2018)
- [Nonparametric method for space conditional density estimation in moderately large dimensions](https://mlsanity.com/paper/1801.06477/) (2018)

## Built on by (most cited first, 9 of 9)

- [Algorithms to estimate Shapley value feature attributions](https://mlsanity.com/paper/2207.07605/) (2022)
- [groupShapley: Efficient prediction explanation with Shapley values for feature groups](https://mlsanity.com/paper/2106.12228/) (2021)
- [Using Shapley Values and Variational Autoencoders to Explain Predictive Models with Dependent Mixed Features](https://mlsanity.com/paper/2111.13507/) (2021)
- [A Comparative Study of Methods for Estimating Conditional Shapley Values and When to Use Them](https://mlsanity.com/paper/2305.09536/) (2023)
- [Accurate Shapley Values for explaining tree-based models](https://mlsanity.com/paper/2106.03820/) (2021)
- [Shapley Curves: A Smoothing Perspective](https://mlsanity.com/paper/2211.13289/) (2022)
- [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)
- [Vine Copulas as Differentiable Computational Graphs](https://mlsanity.com/paper/2506.13318/) (2025)

## Abstract (arXiv)

The original development of Shapley values for prediction explanation relied on the assumption that the features being described were independent. If the features in reality are dependent this may lead to incorrect explanations. Hence, there have recently been attempts of appropriately modelling/estimating the dependence between the features. Although the proposed methods clearly outperform the traditional approach assuming independence, they have their weaknesses. In this paper we propose two new approaches for modelling the dependence between the features. Both approaches are based on vine copulas, which are flexible tools for modelling multivariate non-Gaussian distributions able to characterise a wide range of complex dependencies. The performance of the proposed methods is evaluated on simulated data sets and a real data set. The experiments demonstrate that the vine copula approaches give more accurate approximations to the true Shapley values than its competitors.