# Monotone Tree-Based GAMI Models by Adapting XGBoost

arXiv: https://arxiv.org/abs/2309.02426 · HTML: https://mlsanity.com/paper/2309.02426/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 22 references that are in the map.
- First posted on arXiv 5 Sep 2023.

## Builds on (most cited first, 10 of 10)

- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Neural Additive Models: Interpretable Machine Learning with Neural Nets](https://mlsanity.com/paper/2004.13912/) (2020)
- [GAMI-Net: An Explainable Neural Network based on Generalized Additive Models with Structured Interactions](https://mlsanity.com/paper/2003.07132/) (2020)
- [Certified Monotonic Neural Networks](https://mlsanity.com/paper/2011.10219/) (2020)
- [Explainable Neural Networks based on Additive Index Models](https://mlsanity.com/paper/1806.01933/) (2018)
- [Surrogate Locally-Interpretable Models with Supervised Machine Learning Algorithms](https://mlsanity.com/paper/2007.14528/) (2020)
- [Explaining Adverse Actions in Credit Decisions Using Shapley Decomposition](https://mlsanity.com/paper/2204.12365/) (2022)
- [Interpretable Machine Learning based on Functional ANOVA Framework: Algorithms and Comparisons](https://mlsanity.com/paper/2305.15670/) (2023)
- [Prediction Rule Reshaping](https://mlsanity.com/paper/1805.06439/) (2018)
- [Using Model-Based Trees with Boosting to Fit Low-Order Functional ANOVA Models](https://mlsanity.com/paper/2207.06950/) (2022)

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

- [AMBIT: Augmenting Mobility Baselines with Interpretable Trees](https://mlsanity.com/paper/2512.22466/) (2025)

## Abstract (arXiv)

Recent papers have used machine learning architecture to fit low-order functional ANOVA models with main effects and second-order interactions. These GAMI (GAM + Interaction) models are directly interpretable as the functional main effects and interactions can be easily plotted and visualized. Unfortunately, it is not easy to incorporate the monotonicity requirement into the existing GAMI models based on boosted trees, such as EBM (Lou et al. 2013) and GAMI-Lin-T (Hu et al. 2022). This paper considers models of the form f(x)=sumj,kfj,k(xj, xk) and develops monotone tree-based GAMI models, called monotone GAMI-Tree, by adapting the XGBoost algorithm. It is straightforward to fit a monotone model to f(x) using the options in XGBoost. However, the fitted model is still a black box. We take a different approach: i) use a filtering technique to determine the important interactions, ii) fit a monotone XGBoost algorithm with the selected interactions, and finally iii) parse and purify the results to get a monotone GAMI model. Simulated datasets are used to demonstrate the behaviors of mono-GAMI-Tree and EBM, both of which use piecewise constant fits. Note that the monotonicity requirement is for the full model. Under certain situations, the main effects will also be monotone. But, as seen in the examples, the interactions will not be monotone.