  Estimating the uncertainty of deep learning models in a reliable and
efficient way has remained an open problem, where many different solutions have
been proposed in the literature. Most common methods are based on Bayesian
approximations, like Monte Carlo dropout (MCDO) or Deep ensembling (DE), but
they have a high inference time (i.e. require multiple inference passes) and
might not work for out-of-distribution detection (OOD) data (i.e. similar
uncertainty for in-distribution (ID) and OOD). In safety critical environments,
like medical applications, accurate and fast uncertainty estimation methods,
able to detect OOD data, are crucial, since wrong predictions can jeopardize
patients safety. In this study, we present an alternative direct uncertainty
estimation method and apply it for a regression U-Net architecture. The method
consists in the addition of a branch from the bottleneck which reconstructs the
input. The input reconstruction error can be used as a surrogate of the model
uncertainty. For the proof-of-concept, our method is applied to proton therapy
dose prediction in head and neck cancer patients. Accuracy, time-gain, and OOD
detection are analyzed for our method in this particular application and
compared with the popular MCDO and DE. The input reconstruction method showed a
higher Pearson correlation coefficient with the prediction error (0.620) than
DE and MCDO (between 0.447 and 0.612). Moreover, our method allows an easier
identification of OOD (Z-score of 34.05). It estimates the uncertainty
simultaneously to the regression task, therefore requires less time or
computational resources.
