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Deep regression is an important problem with numerous applications. Theserange from computer vision tasks such as age estimation from photographs, tomedical tasks such as ejection fraction estimation from echocardiograms fordisease tracking. Semi-supervised approaches for deep regression are notablyunder-explored compared to classification and segmentation tasks, however.Unlike classification tasks, which rely on thresholding functions forgenerating class pseudo-labels, regression tasks use real number targetpredictions directly as pseudo-labels, making them more sensitive to predictionquality. In this work, we propose a novel approach to semi-supervisedregression, namely Uncertainty-Consistent Variational Model Ensembling (UCVME),which improves training by generating high-quality pseudo-labels anduncertainty estimates for heteroscedastic regression. Given that aleatoricuncertainty is only dependent on input data by definition and should be equalfor the same inputs, we present a novel uncertainty consistency loss forco-trained models. Our consistency loss significantly improves uncertaintyestimates and allows higher quality pseudo-labels to be assigned greaterimportance under heteroscedastic regression. Furthermore, we introduce a novelvariational model ensembling approach to reduce prediction noise and generatemore robust pseudo-labels. We analytically show our method generates higherquality targets for unlabeled data and further improves training. Experimentsshow that our method outperforms state-of-the-art alternatives on differenttasks and can be competitive with supervised methods that use full labels. Ourcode is available at https://github.com/xmed-lab/UCVME.

Semi-Supervised Deep Regression with Uncertainty Consistency and Variational Model Ensembling via Bayesian Neural Networks