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Response versus gradient boosting trees, GLMs and neural networks under Tweedie loss and log-link

Author

Listed:
  • Hainaut, Donatien

    (Université catholique de Louvain, LIDAM/ISBA, Belgium)

  • Trufin, Julien

    (Université Libre de Bruxelles)

  • Denuit, Michel

    (Université catholique de Louvain, LIDAM/ISBA, Belgium)

Abstract

Thanks to its outstanding performances, boosting has rapidly gained wide acceptance among actuaries. To speed calculations, boosting is often applied to gradients of the loss function, not to responses (hence the name gradient boosting). When the model is trained by minimizing Poisson deviance, this amounts to apply the least-squares principle to raw residuals. This exposes gradient boosting to the same problems that lead to replace least-squares with Poisson GLM to analyze low counts (typically, the number of reported claims at policy level in personal lines). This paper shows that boosting can be conducted directly on the response under Tweedie loss function and log-link, by adapting the weights at each step. Numerical illustrations demonstrate improved performances compared to gradient boosting when trees, GLMs and neural networks are used as weak learners.

Suggested Citation

  • 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).
    • Handle: RePEc:aiz:louvad:2021012
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    References listed on IDEAS

    as
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    4. Denuit, Michel & Hainaut, Donatien & Trufin, Julien, 2020. "Effective Statistical Learning Methods for Actuaries II : Tree-Based Methods and Extensions," LIDAM Reprints ISBA 2020035, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
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    More about this item

    Keywords

    Risk classification ; Boosting ; Gradient Boosting ; Regression Trees ; GLM ; Neural Networks;
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