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{characterize}, and \emph{remove}, the 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 dataset, 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，还来自通常注入大量噪声和偏差的训练过程。这些因素阻碍了统计保证的获得，并且由于需要重复的网络重训练，给不确定性量化带来了计算挑战。基于最新的神经正切核理论，我们构建了具有统计保证的方案，以极低的计算开销原则性地\emph{刻画}并\emph{消除}过参数化神经网络的不确定性。具体而言，我们的方法基于一种称为过程噪声校正（PNC）预测器，仅需使用一个在适当标记数据集上训练的辅助网络（而非深度集成中采用的多个重训练网络），即可消除过程不确定性。此外，通过将PNC预测器与合适的轻量计算重采样方法相结合，我们构建了多种方法，使用低至四个训练网络即可构建渐近精确覆盖率的置信区间，且无额外开销。