# From Point to probabilistic gradient boosting for claim frequency and severity prediction

arXiv: https://arxiv.org/abs/2412.14916 · HTML: https://mlsanity.com/paper/2412.14916/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 73 references that are in the map.
- First posted on arXiv 19 Dec 2024.

## Builds on (most cited first, 20 of 20)

- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [InterpretML: A Unified Framework for Machine Learning Interpretability](https://mlsanity.com/paper/1909.09223/) (2019)
- [CatBoost: gradient boosting with categorical features support](https://mlsanity.com/paper/1810.11363/) (2018)
- [NGBoost: Natural Gradient Boosting for Probabilistic Prediction](https://mlsanity.com/paper/1910.03225/) (2019)
- [Of Quantiles and Expectiles: Consistent Scoring Functions, Choquet Representations, and Forecast Rankings](https://mlsanity.com/paper/1503.08195/) (2015)
- [Probabilistic Gradient Boosting Machines for Large-Scale Probabilistic Regression](https://mlsanity.com/paper/2106.01682/) (2021)
- [Autocalibration and Tweedie-dominance for Insurance Pricing with Machine Learning](https://mlsanity.com/paper/2103.03635/) (2021)
- [Boosting insights in insurance tariff plans with tree-based machine learning methods](https://mlsanity.com/paper/1904.10890/) (2019)
- [Gradient boosting for extreme quantile regression](https://mlsanity.com/paper/2103.00808/) (2021)
- [DART: Dropouts meet Multiple Additive Regression Trees](https://mlsanity.com/paper/1505.01866/) (2015)
- [Gradient and Newton Boosting for Classification and Regression](https://mlsanity.com/paper/1808.03064/) (2018)
- [Model Comparison and Calibration Assessment: User Guide for Consistent Scoring Functions in Machine Learning and Actuarial Practice](https://mlsanity.com/paper/2202.12780/) (2022)
- [XGBoostLSS -- An extension of XGBoost to probabilistic forecasting](https://mlsanity.com/paper/1907.03178/) (2019)
- [Isotonic Recalibration under a Low Signal-to-Noise Ratio](https://mlsanity.com/paper/2301.02692/) (2023)
- [Neural networks for insurance pricing with frequency and severity data: a benchmark study from data preprocessing to technical tariff](https://mlsanity.com/paper/2310.12671/) (2023)
- [Enhanced Gradient Boosting for Zero-Inflated Insurance Claims and Comparative Analysis of CatBoost, XGBoost, and LightGBM](https://mlsanity.com/paper/2307.07771/) (2023)
- [Why You Should Not Trust Interpretations in Machine Learning: Adversarial Attacks on Partial Dependence Plots](https://mlsanity.com/paper/2404.18702/) (2024)
- [CatBoostLSS -- An extension of CatBoost to probabilistic forecasting](https://mlsanity.com/paper/2001.02121/) (2020)
- [Double Probability Integral Transform Residuals for Regression Models with Discrete Outcomes](https://mlsanity.com/paper/2308.15596/) (2023)
- [Zero-Inflated Tweedie Boosted Trees with CatBoost for Insurance Loss Analytics](https://mlsanity.com/paper/2406.16206/) (2024)

## 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)

Gradient boosting for decision tree algorithms are increasingly used in actuarial applications as they show superior predictive performance over traditional generalised linear models. Many enhancements to the first gradient boosting machine algorithm exist. We present in a unified notation, and contrast, all the existing point and probabilistic gradient boosting for decision tree algorithms: GBM, XGBoost, DART, LightGBM, CatBoost, EGBM, PGBM, XGBoostLSS, cyclic GBM, and NGBoost. In this comprehensive numerical study, we compare their performance on five publicly available datasets for claim frequency and severity, of various sizes and comprising different numbers of (high cardinality) categorical variables. We explain how varying exposure-to-risk can be handled with boosting in frequency models. We compare the algorithms on the basis of computational efficiency, predictive performance, and model adequacy. LightGBM and XGBoostLSS win in terms of computational efficiency. CatBoost sometimes improves predictive performance, especially in the presence of high cardinality categorical variables, common in actuarial science. The fully interpretable EGBM achieves competitive predictive performance compared to the black box algorithms considered. We find that there is no trade-off between model adequacy and predictive accuracy: both are achievable simultaneously.