  This paper proposes a fast and scalable method for uncertainty quantification
of machine learning models' predictions. First, we show the principled way to
measure the uncertainty of predictions for a classifier based on
Nadaraya-Watson's nonparametric estimate of the conditional label distribution.
Importantly, the proposed approach allows to disentangle explicitly aleatoric
and epistemic uncertainties. The resulting method works directly in the feature
space. However, one can apply it to any neural network by considering an
embedding of the data induced by the network. We demonstrate the strong
performance of the method in uncertainty estimation tasks on text
classification problems and a variety of real-world image datasets, such as
MNIST, SVHN, CIFAR-100 and several versions of ImageNet.
