# Generalized XGBoost Method

arXiv: https://arxiv.org/abs/2109.07473 · HTML: https://mlsanity.com/paper/2109.07473/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 7 references that are in the map.
- First posted on arXiv 15 Sep 2021.

## Builds on (most cited first, 3 of 3)

- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [CatBoost: gradient boosting with categorical features support](https://mlsanity.com/paper/1810.11363/) (2018)
- [NGBoost: Natural Gradient Boosting for Probabilistic Prediction](https://mlsanity.com/paper/1910.03225/) (2019)

## Abstract (arXiv)

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.