# Function Trees: Transparent Machine Learning

arXiv: https://arxiv.org/abs/2403.13141 · HTML: https://mlsanity.com/paper/2403.13141/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 24 references that are in the map.
- First posted on arXiv 19 Mar 2024.

## Builds on (most cited first, 6 of 6)

- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Visualizing the Effects of Predictor Variables in Black Box Supervised Learning Models](https://mlsanity.com/paper/1612.08468/) (2016)
- [Purifying Interaction Effects with the Functional ANOVA: An Efficient Algorithm for Recovering Identifiable Additive Models](https://mlsanity.com/paper/1911.04974/) (2019)
- [Considerations When Learning Additive Explanations for Black-Box Models](https://mlsanity.com/paper/1801.08640/) (2018)
- [Interpretable Machine Learning based on Functional ANOVA Framework: Algorithms and Comparisons](https://mlsanity.com/paper/2305.15670/) (2023)
- [PDD-SHAP: Fast Approximations for Shapley Values using Functional Decomposition](https://mlsanity.com/paper/2208.12595/) (2022)

## Built on by (most cited first, 1 of 1)

- [FINCH: Locally Visualizing Higher-Order Feature Interactions in Black Box Models](https://mlsanity.com/paper/2503.16445/) (2025)

## Abstract (arXiv)

The output of a machine learning algorithm can usually be represented by one or more multivariate functions of its input variables. Knowing the global properties of such functions can help in understanding the system that produced the data as well as interpreting and explaining corresponding model predictions. A method is presented for representing a general multivariate function as a tree of simpler functions. This tree exposes the global internal structure of the function by uncovering and describing the combined joint influences of subsets of its input variables. Given the inputs and corresponding function values, a function tree is constructed that can be used to rapidly identify and compute all of the function's main and interaction effects up to high order. Interaction effects involving up to four variables are graphically visualized.