Generalized XGBoost Method
This work addresses a specific bottleneck in machine learning for domains requiring non-convex loss functions, such as insurance pricing, but is incremental as it builds directly on XGBoost.
The authors tackled the limitation of XGBoost's loss function being restricted to convex functions by proposing a generalized XGBoost method that accommodates both convex and non-convex loss functions, extending it to multivariate cases for applications like non-life insurance pricing.
The XGBoost method has many advantages and is especially suitable for statistical analysis of big data, but its loss function is limited to convex functions. In many specific applications, a nonconvex loss function would be preferable. In this paper, I propose a generalized XGBoost method, which requires weaker loss function constraint and involves more general loss functions, including convex loss functions and some non-convex loss functions. Furthermore, this generalized XGBoost method is extended to multivariate loss function to form a more generalized XGBoost method. This method is a multiobjective parameter regularized tree boosting method, which can model multiple parameters in most of the frequently-used parametric probability distributions to be fitted by predictor variables. Meanwhile, the related algorithms and some examples in non-life insurance pricing are given.