# A tree-based varying coefficient model

arXiv: https://arxiv.org/abs/2401.05982 · HTML: https://mlsanity.com/paper/2401.05982/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 32 references that are in the map.
- First posted on arXiv 11 Jan 2024.

## Builds on (most cited first, 7 of 7)

- [Towards Robust Interpretability with Self-Explaining Neural Networks](https://mlsanity.com/paper/1806.07538/) (2018)
- [NGBoost: Natural Gradient Boosting for Probabilistic Prediction](https://mlsanity.com/paper/1910.03225/) (2019)
- [Contextual Explanation Networks](https://mlsanity.com/paper/1705.10301/) (2017)
- [LocalGLMnet: interpretable deep learning for tabular data](https://mlsanity.com/paper/2107.11059/) (2021)
- [The Contextual Lasso: Sparse Linear Models via Deep Neural Networks](https://mlsanity.com/paper/2302.00878/) (2023)
- [A Tree-based Semi-Varying Coefficient Model for the COM-Poisson Distribution](https://mlsanity.com/paper/2004.11810/) (2020)
- [Tree-Structured Modelling of Varying Coefficients](https://mlsanity.com/paper/1705.08699/) (2017)

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

- [Explainable Boosting Machine for Predicting Claim Severity and Frequency in Car Insurance](https://mlsanity.com/paper/2503.21321/) (2025)

## Abstract (arXiv)

The paper introduces a tree-based varying coefficient model (VCM) where the varying coefficients are modelled using the cyclic gradient boosting machine (CGBM) from Delong et al. (2023). Modelling the coefficient functions using a CGBM allows for dimension-wise early stopping and feature importance scores. The dimension-wise early stopping not only reduces the risk of dimension-specific overfitting, but also reveals differences in model complexity across dimensions. The use of feature importance scores allows for simple feature selection and easy model interpretation. The model is evaluated on the same simulated and real data examples as those used in Richman and W"uthrich (2023), and the results show that it produces results in terms of out of sample loss that are comparable to those of their neural network-based VCM called LocalGLMnet.