Data imbalance exists ubiquitously in real-world visual regressions, e.g.,
age estimation and pose estimation, hurting the model's generalizability and
fairness. Thus, imbalanced regression gains increasing research attention
recently. Compared to imbalanced classification, imbalanced regression focuses
on continuous labels, which can be boundless and high-dimensional and hence
more challenging. In this work, we identify that the widely used Mean Square
Error (MSE) loss function can be ineffective in imbalanced regression. We
revisit MSE from a statistical view and propose a novel loss function, Balanced
MSE, to accommodate the imbalanced training label distribution. We further
design multiple implementations of Balanced MSE to tackle different real-world
scenarios, particularly including the one that requires no prior knowledge
about the training label distribution. Moreover, to the best of our knowledge,
Balanced MSE is the first general solution to high-dimensional imbalanced
regression. Extensive experiments on both synthetic and three real-world
benchmarks demonstrate the effectiveness of Balanced MSE.

本研究在统计学角度重新审视了广泛采用的均方误差（MSE）损失函数，指出它不适用于不平衡回归问题，并提出了一种新的平衡 MSE 损失函数来解决高维度的不平衡回归训练标签分布问题。在多个实际场景中，Balanced MSE 表现卓越，是高维不平衡回归的第一个通用解决方案。