Generalized XGBoost Method

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, we propose a generalized XGBoost method, which requires weaker loss function condition 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 multivariate 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.