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Estimating the uncertainty of deep learning models in a reliable andefficient way has remained an open problem, where many different solutions havebeen proposed in the literature. Most common methods are based on Bayesianapproximations, like Monte Carlo dropout (MCDO) or Deep ensembling (DE), butthey have a high inference time (i.e. require multiple inference passes) andmight not work for out-of-distribution detection (OOD) data (i.e. similaruncertainty 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 jeopardizepatients safety. In this study, we present an alternative direct uncertaintyestimation method and apply it for a regression U-Net architecture. The methodconsists in the addition of a branch from the bottleneck which reconstructs theinput. The input reconstruction error can be used as a surrogate of the modeluncertainty. For the proof-of-concept, our method is applied to proton therapydose prediction in head and neck cancer patients. Accuracy, time-gain, and OODdetection are analyzed for our method in this particular application andcompared with the popular MCDO and DE. The input reconstruction method showed ahigher Pearson correlation coefficient with the prediction error (0.620) thanDE and MCDO (between 0.447 and 0.612). Moreover, our method allows an easieridentification of OOD (Z-score of 34.05). It estimates the uncertaintysimultaneously to the regression task, therefore requires less time orcomputational resources.

Can input reconstruction be used to directly estimate uncertainty of a  regression U-Net model? -- Application to proton therapy dose prediction for  head and neck cancer patients