From point to probabilistic gradient boosting for claim frequency and severity prediction.

Area of Science:

• Actuarial Science
• Machine Learning
• Data Science

Background:

• Gradient boosting decision tree algorithms are increasingly favored in actuarial applications due to their superior predictive performance compared to traditional generalized linear models.
• Numerous enhancements to the initial gradient boosting machine algorithm have been developed.

Purpose of the Study:

• To present a unified notation and contrast existing point and probabilistic gradient boosting for decision tree algorithms.
• To conduct a comprehensive numerical comparison of these algorithms on actuarial datasets.

Main Methods:

• A comparative numerical study of eleven gradient boosting algorithms: GBM, XGBoost, DART, LightGBM, CatBoost, EGBM, PGBM, XGBoostLSS, cyclic GBM, and NGBoost.
• Evaluation on five public datasets for claim frequency and severity, considering variable sizes and high-cardinality categorical variables.
• Analysis of computational efficiency, predictive performance, and model adequacy, including handling varying exposure-to-risk in frequency models.

Main Results:

• LightGBM and XGBoostLSS demonstrated superior computational efficiency.
• CatBoost showed improved predictive performance, particularly with high-cardinality categorical variables.
• The interpretable EGBM achieved competitive predictive performance against black-box models.

Conclusions:

• No trade-off exists between model adequacy and predictive accuracy in gradient boosting algorithms; both can be achieved simultaneously.
• Algorithm choice impacts computational efficiency and predictive performance, especially concerning categorical variable handling in actuarial modeling.