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

TL;DR

This paper compares various point and probabilistic gradient boosting algorithms for claim frequency and severity prediction, highlighting their performance, efficiency, and interpretability in actuarial datasets.

Contribution

It provides a unified comparison of existing gradient boosting methods, including new insights on handling exposure-to-risk and model interpretability in actuarial applications.

Findings

LightGBM and XGBoostLSS are most computationally efficient.

CatBoost performs well with high cardinality categorical variables.

EGBM offers competitive interpretability without sacrificing accuracy.

Abstract

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.