Regression plays an essential role in many medical imaging applications for estimating various clinical risk or measurement scores. While training strategies and loss functions have been studied for the deep neural networks in medical image classification tasks, options for regression tasks are very limited. One of the key challenges is that the high-dimensional feature representation learned by existing popular loss functions like Mean Squared Error or L1 loss is hard to interpret. In this paper, we propose a novel Regression Metric Loss (RM-Loss), which endows the representation space with the semantic meaning of the label space by finding a representation manifold that is isometric to the label space. Experiments on two regression tasks, i.e. coronary artery calcium score estimation and bone age assessment, show that RM-Loss is superior to the existing popular regression losses on both performance and interpretability. Code is available at https://github.com/DIAL-RPI/Regression-Metric-Loss.
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