  This paper introduces Conformal Thresholded Intervals (CTI), a novel
conformal regression method that aims to produce the smallest possible
prediction set with guaranteed coverage. Unlike existing methods that rely on
nested conformal framework and full conditional distribution estimation, CTI
estimates the conditional probability density for a new response to fall into
each interquantile interval using off-the-shelf multi-output quantile
regression. CTI constructs prediction sets by thresholding the estimated
conditional interquantile intervals based on their length, which is inversely
proportional to the estimated probability density. The threshold is determined
using a calibration set to ensure marginal coverage. Experimental results
demonstrate that CTI achieves optimal performance across various datasets.
