Frequentist uncertainty estimates for deep learning

We provide frequentist estimates of aleatoric and epistemic uncertainty for deep neural networks. To estimate aleatoric uncertainty we propose simultaneous quantile regression, a loss function to learn all the conditional quantiles of a given target variable. These quantiles lead to well-calibrated prediction intervals. To estimate epistemic uncertainty we propose training certificates, a collection of diverse non-trivial functions that map all training samples to zero. These certificates map out-of-distribution examples to non-zero values, signaling high epistemic uncertainty. We compare our proposals to prior art in various experiments.