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

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.