  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 20% while achieving the same
or better coverage probability
