Uncertainty quantification (UQ) is important for reliability assessment and enhancement of machine learning models. In deep learning, uncertainties arise not only from data, but also from the training procedure that often injects substantial noises and biases. These hinder the attainment of statistical guarantees and, moreover, impose computational challenges on UQ due to the need for repeated network retraining. Building upon the recent neural tangent kernel theory, we create statistically guaranteed schemes to principally \emph{quantify}, and \emph{remove}, the procedural uncertainty of over-parameterized neural networks with very low computation effort. In particular, our approach, based on what we call a procedural-noise-correcting (PNC) predictor, removes the procedural uncertainty by using only \emph{one} auxiliary network that is trained on a suitably labeled data set, instead of many retrained networks employed in deep ensembles. Moreover, by combining our PNC predictor with suitable light-computation resampling methods, we build several approaches to construct asymptotically exact-coverage confidence intervals using as low as four trained networks without additional overheads.

翻译：不确定性量化对于机器学习模型的可靠性评估与增强至关重要。在深度学习中，不确定性不仅源于数据，还来自于通常注入大量噪声和偏差的训练过程。这些因素不仅阻碍了统计保证的获得，还因需要重复的网络再训练而对不确定性量化提出了计算挑战。基于近期提出的神经正切核理论，我们创建了具有统计保证的方案，以较低的计算开销原则性地量化并消除过参数化神经网络的程序不确定性。具体而言，我们的方法基于一种称为程序噪声校正（PNC）预测器的方案，通过仅训练一个在适当标注数据集上的辅助网络来消除程序不确定性，而非采用深度集成中需要的大量再训练网络。此外，通过将PNC预测器与适合低计算量的重采样方法相结合，我们构建了多种方法，仅使用四个（无需额外开销）训练网络即可构建渐近精确覆盖率的置信区间。