Imbalanced learning for insurance using modified loss functions in tree-based models

Changyue Hu, Zhiyu Quan*, Wing Fung Chong

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)
34 Downloads (Pure)


Tree-based models have gained momentum in insurance claim loss modeling; however, the point mass at zero and the heavy tail of insurance loss distribution pose the challenge to apply conventional methods directly to claim loss modeling. With a simple illustrative dataset, we first demonstrate how the traditional tree-based algorithm's splitting function fails to cope with a large proportion of data with zero responses. To address the imbalance issue presented in such loss modeling, this paper aims to modify the traditional splitting function of Classification and Regression Tree (CART). In particular, we propose two novel modified loss functions, namely, the weighted sum of squared error and the sum of squared Canberra error. These modified loss functions impose a significant penalty on grouping observations of non-zero response with those of zero response at the splitting procedure, and thus significantly enhance their separation. Finally, we examine and compare the predictive performance of such modified tree-based models to the traditional model on synthetic datasets that imitate insurance loss. The results show that such modification leads to substantially different tree structures and improved prediction performance.

Original languageEnglish
Pages (from-to)13-32
Number of pages20
JournalInsurance: Mathematics and Economics
Early online date28 Apr 2022
Publication statusPublished - Sept 2022


  • Canberra distance
  • Custom loss
  • Imbalanced learning
  • Predictive model of insurance claims
  • Regression tree
  • Tree-based algorithms

ASJC Scopus subject areas

  • Statistics and Probability
  • Economics and Econometrics
  • Statistics, Probability and Uncertainty


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