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By seeking the narrowest prediction intervals (PIs) that satisfy thespecified coverage probability requirements, the recently proposedquality-based PI learning principle can extract high-quality PIs that bettersummarize the predictive certainty in regression tasks, and has been widelyapplied to solve many practical problems. Currently, the state-of-the-artquality-based PI estimation methods are based on deep neural networks or linearmodels. In this paper, we propose Highest Density Interval Regression Forest(HDI-Forest), a novel quality-based PI estimation method that is instead basedon Random Forest. HDI-Forest does not require additional model training, anddirectly reuses the trees learned in a standard Random Forest model. Byutilizing the special properties of Random Forest, HDI-Forest could efficientlyand more directly optimize the PI quality metrics. Extensive experiments onbenchmark datasets show that HDI-Forest significantly outperforms previousapproaches, reducing the average PI width by over 20% while achieving the sameor better coverage probability

HDI-Forest: Highest Density Interval Regression Forest