# Explaining predictive models with mixed features using Shapley values and conditional inference trees

arXiv: https://arxiv.org/abs/2007.01027 · HTML: https://mlsanity.com/paper/2007.01027/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Jul 2020.

## Built on by (most cited first, 18 of 18)

- [Algorithms to estimate Shapley value feature attributions](https://mlsanity.com/paper/2207.07605/) (2022)
- [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)
- [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)
- [Ensembles of Random SHAPs](https://mlsanity.com/paper/2103.03302/) (2021)
- [An Imprecise SHAP as a Tool for Explaining the Class Probability Distributions under Limited Training Data](https://mlsanity.com/paper/2106.09111/) (2021)
- [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)
- [Inferring feature importance with uncertainties in high-dimensional data](https://mlsanity.com/paper/2109.00855/) (2021)
- [A Comprehensive Study of Shapley Value in Data Analytics](https://mlsanity.com/paper/2412.01460/) (2024)
- [What's Wrong with Your Synthetic Tabular Data? Using Explainable AI to Evaluate Generative Models](https://mlsanity.com/paper/2504.20687/) (2025)
- [Computing Conditional Shapley Values Using Tabular Foundation Models](https://mlsanity.com/paper/2602.09489/) (2026)
- [xplainfi: Feature Importance and Statistical Inference for Machine Learning in R](https://mlsanity.com/paper/2603.15306/) (2026)
- [Explainable Artificial Intelligence and Multicollinearity : A Mini Review of Current Approaches](https://mlsanity.com/paper/2406.11524/) (2024)
- [Owen-based Semantics and Hierarchy-Aware Explanation (O-Shap)](https://mlsanity.com/paper/2602.17107/) (2026)
- [A New Technique for AI Explainability using Feature Association Map](https://mlsanity.com/paper/2605.12350/) (2026)
- [A Statistical Framework for Data-Driven Discovery of Differential Performance in Clinical Risk Prediction Models](https://mlsanity.com/paper/2608.01333/) (2026)

## Abstract (arXiv)

It is becoming increasingly important to explain complex, black-box machine learning models. Although there is an expanding literature on this topic, Shapley values stand out as a sound method to explain predictions from any type of machine learning model. The original development of Shapley values for prediction explanation relied on the assumption that the features being described were independent. This methodology was then extended to explain dependent features with an underlying continuous distribution. In this paper, we propose a method to explain mixed (i.e. continuous, discrete, ordinal, and categorical) dependent features by modeling the dependence structure of the features using conditional inference trees. We demonstrate our proposed method against the current industry standards in various simulation studies and find that our method often outperforms the other approaches. Finally, we apply our method to a real financial data set used in the 2018 FICO Explainable Machine Learning Challenge and show how our explanations compare to the FICO challenge Recognition Award winning team.