  By generating prediction intervals (PIs) to quantify the uncertainty of each
prediction in deep learning regression, the risk of wrong predictions can be
effectively controlled. High-quality PIs need to be as narrow as possible,
whilst covering a preset proportion of real labels. At present, many approaches
to improve the quality of PIs can effectively reduce the width of PIs, but they
do not ensure that enough real labels are captured. Inductive Conformal
Predictor (ICP) is an algorithm that can generate effective PIs which is
theoretically guaranteed to cover a preset proportion of data. However,
typically ICP is not directly optimized to yield minimal PI width. However, in
this study, we use Directly Optimized Inductive Conformal Regression (DOICR)
that takes only the average width of PIs as the loss function and increases the
quality of PIs through an optimized scheme under the validity condition that
sufficient real labels are captured in the PIs. Benchmark experiments show that
DOICR outperforms current state-of-the-art algorithms for regression problems
using underlying Deep Neural Network structures for both tabular and image
data.
