Deep regression is an important problem with numerous applications. These range from computer vision tasks such as age estimation from photographs, to medical tasks such as ejection fraction estimation from echocardiograms for disease tracking. Semi-supervised approaches for deep regression are notably under-explored compared to classification and segmentation tasks, however. Unlike classification tasks, which rely on thresholding functions for generating class pseudo-labels, regression tasks use real number target predictions directly as pseudo-labels, making them more sensitive to prediction quality. In this work, we propose a novel approach to semi-supervised regression, namely Uncertainty-Consistent Variational Model Ensembling (UCVME), which improves training by generating high-quality pseudo-labels and uncertainty estimates for heteroscedastic regression. Given that aleatoric uncertainty is only dependent on input data by definition and should be equal for the same inputs, we present a novel uncertainty consistency loss for co-trained models. Our consistency loss significantly improves uncertainty estimates and allows higher quality pseudo-labels to be assigned greater importance under heteroscedastic regression. Furthermore, we introduce a novel variational model ensembling approach to reduce prediction noise and generate more robust pseudo-labels. We analytically show our method generates higher quality targets for unlabeled data and further improves training. Experiments show that our method outperforms state-of-the-art alternatives on different tasks and can be competitive with supervised methods that use full labels. Our code is available at https://github.com/xmed-lab/UCVME.

翻译：深度回归是一个重要问题，具有众多应用场景，涵盖从计算机视觉任务（如基于照片的年龄估计）到医学任务（如通过超声心动图估计射血分数以追踪疾病进展）。然而，与分类和分割任务相比，半监督深度回归方法的研究明显不足。不同于依赖阈值函数生成类别伪标签的分类任务，回归任务直接使用实数值目标预测作为伪标签，这使得其对预测质量更为敏感。本文提出一种新型半监督回归方法——不确定性一致性变分模型集成（UCVME），该方法通过生成高质量伪标签和异方差回归的不确定性估计来改进训练过程。鉴于偶然不确定性在定义上仅依赖于输入数据，且对于相同输入应保持一致性，我们提出了一种用于联合训练模型的新型不确定性一致性损失函数。该一致性损失函数显著提升了不确定性估计质量，使得在异方差回归中能为高质量伪标签赋予更高权重。此外，我们引入了一种新型变分模型集成方法以降低预测噪声并生成更稳健的伪标签。理论分析表明，我们的方法能为无标签数据生成更优质的目标值并进一步优化训练过程。实验证明，该方法在不同任务上均优于现有最优方法，且能与使用完整标签的有监督方法相媲美。我们的代码已开源在 https://github.com/xmed-lab/UCVME。