Monotone Composite Quantile Regression via Second-Order Gradient Boosting Framework

초록

Second-order gradient boosting methods have shown strong empirical performance in a wide range of regression and classification tasks. However, their application in quantile regression has been limited due to the zero second derivatives of the quantile loss and crossing quantiles. In this study, we explore these challenges in second-order boosting for quantile prediction and propose a new algorithm for estimating multiple conditional quantiles that exploits second-order information while enforcing the non-crossing property. In particular, our approach produces non-crossing quantile estimates without solving an explicitly constrained optimization problem. Moreover, the proposed method inherits the computational efficiency of standard second-order gradient boosting frameworks such as XGBoost and LightGBM. Experiments on simulated and real-world datasets show that our method is competitive with state-of-the-art alternatives and yields improved accuracy and stability for multiple quantile estimation.

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