MQBoost is a gradient boosting-based framework for simultaneous multi-quantile regression with monotonicity constraints (non-crossing quantiles). It is built on top of LightGBM and XGBoost, two leading gradient boosting frameworks, enabling efficient and scalable training while ensuring valid quantile estimates.
Standard quantile regression models often suffer from quantile crossing (e.g., 90% quantile < 50% quantile) and independent training per quantile → inconsistent predictions. We solve this by:
- Learning multiple quantiles jointly
- Enforcing monotonicity across quantiles
- Leveraging efficient boosting frameworks
Install using pip:
pip install mqboost- MQDataset: Encapsulates the dataset used for MQRegressor.
- MQRegressor: Custom multiple quantile estimator with preserving monotonicity among quantiles.
Please refer to the 
If you use MQBoost in your research or project, please cite it as follows:
@article{moon2026monotone,
title={Monotone Composite Quantile Regression via Second-Order Gradient Boosting Framework},
author={Moon, Sangjun and Hong, Sungchul and Park, Beomjin},
journal={Machine Learning},
volume={115},
number={6},
pages={127},
year={2026},
publisher={Springer}
}