Boosting on the responses with tweedie and binomial loss functions

Boosting emerged from the field of machine learning and became rapidly popular among insurance analysts. The Tweedie and Binomial distributions are the most commonly used in insurance for regression analysis. Hainaut et al. (2022) showed that boosting can be conducted directly on the response under Tweedie loss function and log-link, by adapting the weights at each iteration step. In this note, we recall the results of Hainaut et al. (2022) and we supplement them with an easy probabilistic interpretation to the boosting procedure. Next, we draw a parallel between these results and those established by Hastie et al. (2009) for the Bernoulli loss function and logit-link: Hastie et al. (2009) highlighted that, as an approximation, boosting can also be performed directly with responses under Bernoulli loss function and logit-link. Interestingly, we show that this observation can actually been extended to the Binomial case.

Keywords: Clustering analysis, unsupervised learning, k-means, spectral clustering.