  As the availability, size and complexity of data have increased in recent
years, machine learning (ML) techniques have become popular for modeling.
Predictions resulting from applying ML models are often used for inference,
decision-making, and downstream applications. A crucial yet often overlooked
aspect of ML is uncertainty quantification, which can significantly impact how
predictions from models are used and interpreted.
  Extreme Gradient Boosting (XGBoost) is one of the most popular ML methods
given its simple implementation, fast computation, and sequential learning,
which make its predictions highly accurate compared to other methods. However,
techniques for uncertainty determination in ML models such as XGBoost have not
yet been universally agreed among its varying applications. We propose
enhancements to XGBoost whereby a modified quantile regression is used as the
objective function to estimate uncertainty (QXGBoost). Specifically, we
included the Huber norm in the quantile regression model to construct a
differentiable approximation to the quantile regression error function. This
key step allows XGBoost, which uses a gradient-based optimization algorithm, to
make probabilistic predictions efficiently.
  QXGBoost was applied to create 90\% prediction intervals for one simulated
dataset and one real-world environmental dataset of measured traffic noise. Our
proposed method had comparable or better performance than the uncertainty
estimates generated for regular and quantile light gradient boosting. For both
the simulated and traffic noise datasets, the overall performance of the
prediction intervals from QXGBoost were better than other models based on
coverage width-based criterion.
