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Delta Boosting Machine with Application to General Insurance

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  • Simon C. K. Lee
  • Sheldon Lin

Abstract

In this article, we introduce Delta Boosting (DB) as a new member of the boosting family. Similar to the popular Gradient Boosting (GB), this new member is presented as a forward stagewise additive model that attempts to reduce the loss at each iteration by sequentially fitting a simple base learner to complement the running predictions. Instead of relying on the negative gradient, as is the case for GB, DB adopts a new measure called delta as the basis. Delta is defined as the loss minimizer at an observation level. We also show that DB is the optimal boosting member for a wide range of loss functions. The optimality is a consequence of DB solving for the split and adjustment simultaneously to maximize loss reduction at each iteration. In addition, we introduce an asymptotic version of DB that works well for all twice-differentiable strictly convex loss functions. This asymptotic behavior does not depend on the number of observations, but rather on a high number of iterations that can be augmented through common regularization techniques. We show that the basis in the asymptotic extension differs from the basis in GB only by a multiple of the second derivative of the log-likelihood. The multiple is considered to be a correction factor, one that corrects the bias toward the observations with high second derivatives in GB. When negative log-likelihood is used as the loss function, this correction can be interpreted as a credibility adjustment for the process variance. Simulation studies and real data application we conducted suggest that DB is a significant improvement over GB. The performance of the asymptotic version is less dramatic, but the improvement is still compelling. Like GB, DB provides a high transparency to users, and we can review the marginal influence of variables through relative importance charts and the partial dependence plots. We can also assess the overall model performance through evaluating the losses, lifts, and double lifts on the holdout sample.

Suggested Citation

  • Simon C. K. Lee & Sheldon Lin, 2018. "Delta Boosting Machine with Application to General Insurance," North American Actuarial Journal, Taylor & Francis Journals, vol. 22(3), pages 405-425, July.
  • Handle: RePEc:taf:uaajxx:v:22:y:2018:i:3:p:405-425
    DOI: 10.1080/10920277.2018.1431131
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    Citations

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    Cited by:

    1. Christopher Blier-Wong & Hélène Cossette & Luc Lamontagne & Etienne Marceau, 2020. "Machine Learning in P&C Insurance: A Review for Pricing and Reserving," Risks, MDPI, vol. 9(1), pages 1-26, December.
    2. Quan Zhiyu & Valdez Emiliano A., 2018. "Predictive analytics of insurance claims using multivariate decision trees," Dependence Modeling, De Gruyter, vol. 6(1), pages 377-407, December.
    3. Trufin, Julien & Denuit, Michel, 2021. "Boosting cost-complexity pruned trees On Tweedie responses: the ABT machine," LIDAM Discussion Papers ISBA 2021015, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    4. Zhiyu Quan & Changyue Hu & Panyi Dong & Emiliano A. Valdez, 2024. "Improving Business Insurance Loss Models by Leveraging InsurTech Innovation," Papers 2401.16723, arXiv.org.
    5. Willame, Gireg & Trufin, Julien & Denuit, Michel, 2023. "Boosted Poisson regression trees: A guide to the BT package in R," LIDAM Discussion Papers ISBA 2023008, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    6. Jessica Pesantez-Narvaez & Montserrat Guillen & Manuela Alcañiz, 2019. "Predicting Motor Insurance Claims Using Telematics Data—XGBoost versus Logistic Regression," Risks, MDPI, vol. 7(2), pages 1-16, June.
    7. Hainaut, Donatien & Trufin, Julien & Denuit, Michel, 2021. "Response versus gradient boosting trees, GLMs and neural networks under Tweedie loss and log-link," LIDAM Discussion Papers ISBA 2021012, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    8. Yang Qiao & Chou-Wen Wang & Wenjun Zhu, 2024. "Machine learning in long-term mortality forecasting," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 49(2), pages 340-362, April.
    9. Simon CK Lee, 2020. "Delta Boosting Implementation of Negative Binomial Regression in Actuarial Pricing," Risks, MDPI, vol. 8(1), pages 1-21, February.
    10. Jessica Pesantez-Narvaez & Montserrat Guillen & Manuela Alcañiz, 2021. "RiskLogitboost Regression for Rare Events in Binary Response: An Econometric Approach," Mathematics, MDPI, vol. 9(5), pages 1-21, March.

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