Pairing an arbitrary regressor with an artificial neural network estimating aleatoric uncertainty

We suggest a general approach to quantification of different types of uncertainty in regression tasks performed by deep neural networks. It is based on the simultaneous training of two neural networks with a joint loss function. One of the networks performs regression and the other quantifies the uncertainty of predictions of the first one. Unlike in many standard uncertainty quantification methods, the targets are not assumed to be sampled from an a priori given probability distribution. We analyze how the hyperparameters affect the learning process and, additionally, show that our method even allows for better predictions compared to standard neural networks without uncertainty counterparts. Finally, we show that a particular case of our approach is the mean-variance estimation given by a Gaussian network.