Contrastive learning methods enforce label distance relationships in feature space to improve representation capability for regression models. However, these methods highly depend on label information to correctly recover ordinal relationships of features, limiting their applications to semi-supervised regression. In this work, we extend contrastive regression methods to allow unlabeled data to be used in the semi-supervised setting, thereby reducing the dependence on costly annotations. Particularly we construct the feature similarity matrix with both labeled and unlabeled samples in a mini-batch to reflect inter-sample relationships, and an accurate ordinal ranking of involved unlabeled samples can be recovered through spectral seriation algorithms if the level of error is within certain bounds. The introduction of labeled samples above provides regularization of the ordinal ranking with guidance from the ground-truth label information, making the ranking more reliable. To reduce feature perturbations, we further utilize the dynamic programming algorithm to select robust features for the matrix construction. The recovered ordinal relationship is then used for contrastive learning on unlabeled samples, and we thus allow more data to be used for feature representation learning, thereby achieving more robust results. The ordinal rankings can also be used to supervise predictions on unlabeled samples, serving as an additional training signal. We provide theoretical guarantees and empirical verification through experiments on various datasets, demonstrating that our method can surpass existing state-of-the-art semi-supervised deep regression methods.

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. Code is available at https://github.com/xmed-lab/UCVME.

Contrastive learning methods can be applied to deep regression by enforcing label distance relationships in feature space. However, these methods are limited to labeled data only unlike for classification, where unlabeled data can be used for contrastive pretraining. In this work, we extend contrastive regression methods to allow unlabeled data to be used in a semi-supervised setting, thereby reducing the reliance on manual annotations. We observe that the feature similarity matrix between unlabeled samples still reflect inter-sample relationships, and that an accurate ordinal relationship can be recovered through spectral seriation algorithms if the level of error is within certain bounds. By using the recovered ordinal relationship for contrastive learning on unlabeled samples, we can allow more data to be used for feature representation learning, thereby achieve more robust results. The ordinal rankings can also be used to supervise predictions on unlabeled samples, which can serve as an additional training signal. We provide theoretical guarantees and empirical support through experiments on different datasets, demonstrating that our method can surpass existing state-of-the-art semi-supervised deep regression methods. To the best of our knowledge, this work is the first to explore using unlabeled data to perform contrastive learning for regression.

Left-ventricular ejection fraction (LVEF) is an important indicator of heart failure. Existing methods for LVEF estimation from video require large amounts of annotated data to achieve high performance, e.g. using 10,030 labeled echocardiogram videos to achieve mean absolute error (MAE) of 4.10. Labeling these videos is time-consuming however and limits potential downstream applications to other heart diseases. This paper presents the first semi-supervised approach for LVEF prediction. Unlike general video prediction tasks, LVEF prediction is specifically related to changes in the left ventricle (LV) in echocardiogram videos. By incorporating knowledge learned from predicting LV segmentations into LVEF regression, we can provide additional context to the model for better predictions. To this end, we propose a novel Cyclical Self-Supervision (CSS) method for learning video-based LV segmentation, which is motivated by the observation that the heartbeat is a cyclical process with temporal repetition. Prediction masks from our segmentation model can then be used as additional input for LVEF regression to provide spatial context for the LV region. We also introduce teacher-student distillation to distill the information from LV segmentation masks into an end-to-end LVEF regression model that only requires video inputs. Results show our method outperforms alternative semi-supervised methods and can achieve MAE of 4.17, which is competitive with state-of-the-art supervised performance, using half the number of labels. Validation on an external dataset also shows improved generalization ability from using our method.

Image regression tasks for medical applications, such as bone mineral density (BMD) estimation and left-ventricular ejection fraction (LVEF) prediction, play an important role in computer-aided disease assessment. Most deep regression methods train the neural network with a single regression loss function like MSE or L1 loss. In this paper, we propose the first contrastive learning framework for deep image regression, namely AdaCon, which consists of a feature learning branch via a novel adaptive-margin contrastive loss and a regression prediction branch. Our method incorporates label distance relationships as part of the learned feature representations, which allows for better performance in downstream regression tasks. Moreover, it can be used as a plug-and-play module to improve performance of existing regression methods. We demonstrate the effectiveness of AdaCon on two medical image regression tasks, i.e., bone mineral density estimation from X-ray images and left-ventricular ejection fraction prediction from echocardiogram videos. AdaCon leads to relative improvements of 3.3% and 5.9% in MAE over state-of-the-art BMD estimation and LVEF prediction methods, respectively.