  Deep learning models have significantly improved prediction accuracy in
various fields, gaining recognition across numerous disciplines. Yet, an aspect
of deep learning that remains insufficiently addressed is the assessment of
prediction uncertainty. Producing reliable uncertainty estimators could be
crucial in practical terms. For instance, predictions associated with a high
degree of uncertainty could be sent for further evaluation. Recent works in
uncertainty quantification of deep learning predictions, including Bayesian
posterior credible intervals and a frequentist confidence-interval estimation,
have proven to yield either invalid or overly conservative intervals.
Furthermore, there is currently no method for quantifying uncertainty that can
accommodate deep neural networks for survival (time-to-event) data that
involves right-censored outcomes. In this work, we provide a valid
non-parametric bootstrap method that correctly disentangles data uncertainty
from the noise inherent in the adopted optimization algorithm, ensuring that
the resulting point-wise confidence intervals or the simultaneous confidence
bands are accurate (i.e., valid and not overly conservative). The proposed
ad-hoc method can be easily integrated into any deep neural network without
interfering with the training process. The utility of the proposed approach is
illustrated by constructing simultaneous confidence bands for survival curves
derived from deep neural networks for survival data with right censoring.
