By seeking the narrowest prediction intervals (PIs) that satisfy the specified coverage probability requirements, the recently proposed quality-based PI learning principle can extract high-quality PIs that better summarize the predictive certainty in regression tasks, and has been widely applied to solve many practical problems. Currently, the state-of-the-art quality-based PI estimation methods are based on deep neural networks or linear models. In this paper, we propose Highest Density Interval Regression Forest (HDI-Forest), a novel quality-based PI estimation method that is instead based on Random Forest. HDI-Forest does not require additional model training, and directly reuses the trees learned in a standard Random Forest model. By utilizing the special properties of Random Forest, HDI-Forest could efficiently and more directly optimize the PI quality metrics. Extensive experiments on benchmark datasets show that HDI-Forest significantly outperforms previous approaches, reducing the average PI width by over 30\% while achieving the same or better coverage probability.

本文提出了一种基于随机森林的新型最高密度区间回归模型（HDI-Forests），用于提高回归任务中预测置信度的质量和效率，并在基准数据集上进行了广泛的实验证明，相较之前的方法，能够将平均 PI 宽度减少20%以上且达到相同或更好的覆盖概率。

HDI-Forest：最高密度区间回归森林