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.

翻译：深度学习模型已在诸多领域显著提升预测准确性，获得多学科广泛认可。然而，深度学习在预测不确定性评估方面仍存在不足。构建可靠的不确定性估计器在实际应用中至关重要，例如，可将具有高度不确定性的预测结果提交进一步评估。近期关于深度学习预测不确定性量化的研究（包括贝叶斯后验可信区间和频率学派的置信区间估计）已被证明会产生无效或过于保守的区间。此外，目前尚无量化的方法能够适用于处理包含右删失结果的生存（事件发生时间）数据的深度神经网络。本研究提出一种有效的非参数自助法，能够正确区分数据不确定性与所采用优化算法固有的噪声，确保所得逐点置信区间或同时置信带具有精确性（即有效且不过度保守）。所提出的专用方法可轻松集成至任意深度神经网络，且不干扰训练过程。通过为右删失生存数据的深度神经网络构建生存曲线的同时置信带，验证了该方法的实用性。