# Balanced MSE for Imbalanced Visual Regression

arXiv: https://arxiv.org/abs/2203.16427 · HTML: https://mlsanity.com/paper/2203.16427/

## Key facts

- Cited by 89 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 52 references that are in the map.
- First posted on arXiv 30 Mar 2022.

## Builds on (most cited first, 30 of 32)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Class-Balanced Loss Based on Effective Number of Samples](https://mlsanity.com/paper/1901.05555/) (2019)
- [LVIS: A Dataset for Large Vocabulary Instance Segmentation](https://mlsanity.com/paper/1908.03195/) (2019)
- [Learning Imbalanced Datasets with Label-Distribution-Aware Margin Loss](https://mlsanity.com/paper/1906.07413/) (2019)
- [End-to-end Recovery of Human Shape and Pose](https://mlsanity.com/paper/1712.06584/) (2017)
- [Decoupling Representation and Classifier for Long-Tailed Recognition](https://mlsanity.com/paper/1910.09217/) (2019)
- [Large-Scale Long-Tailed Recognition in an Open World](https://mlsanity.com/paper/1904.05160/) (2019)
- [Learning to Reconstruct 3D Human Pose and Shape via Model-fitting in the Loop](https://mlsanity.com/paper/1909.12828/) (2019)
- [Long-tail learning via logit adjustment](https://mlsanity.com/paper/2007.07314/) (2020)
- [A systematic study of the class imbalance problem in convolutional neural networks](https://mlsanity.com/paper/1710.05381/) (2017)
- [Monocular 3D Human Pose Estimation In The Wild Using Improved CNN Supervision](https://mlsanity.com/paper/1611.09813/) (2016)
- [BBN: Bilateral-Branch Network with Cumulative Learning for Long-Tailed Visual Recognition](https://mlsanity.com/paper/1912.02413/) (2019)
- [Balanced Meta-Softmax for Long-Tailed Visual Recognition](https://mlsanity.com/paper/2007.10740/) (2020)
- [Long-tailed Recognition by Routing Diverse Distribution-Aware Experts](https://mlsanity.com/paper/2010.01809/) (2020)
- [What is the Effect of Importance Weighting in Deep Learning?](https://mlsanity.com/paper/1812.03372/) (2018)
- [Rethinking the Value of Labels for Improving Class-Imbalanced Learning](https://mlsanity.com/paper/2006.07529/) (2020)
- [Disentangling Label Distribution for Long-tailed Visual Recognition](https://mlsanity.com/paper/2012.00321/) (2020)
- [Delving into Deep Imbalanced Regression](https://mlsanity.com/paper/2102.09554/) (2021)
- [Seesaw Loss for Long-Tailed Instance Segmentation](https://mlsanity.com/paper/2008.10032/) (2020)
- [Revisiting Single Image Depth Estimation: Toward Higher Resolution Maps with Accurate Object Boundaries](https://mlsanity.com/paper/1803.08673/) (2018)
- [Rethinking Class-Balanced Methods for Long-Tailed Visual Recognition from a Domain Adaptation Perspective](https://mlsanity.com/paper/2003.10780/) (2020)
- [Feature Space Augmentation for Long-Tailed Data](https://mlsanity.com/paper/2008.03673/) (2020)
- [M2m: Imbalanced Classification via Major-to-minor Translation](https://mlsanity.com/paper/2004.00431/) (2020)
- [Posterior Re-calibration for Imbalanced Datasets](https://mlsanity.com/paper/2010.11820/) (2020)
- [An Alternative Probabilistic Interpretation of the Huber Loss](https://mlsanity.com/paper/1911.02088/) (2019)

## Built on by (most cited first, 30 of 89)

- [ReMoDiffuse: Retrieval-Augmented Motion Diffusion Model](https://mlsanity.com/paper/2304.01116/) (2023)
- [HOI-M3:Capture Multiple Humans and Objects Interaction within Contextual Environment](https://mlsanity.com/paper/2404.00299/) (2024)
- [Evaluating and Steering Modality Preferences in Multimodal Large Language Model](https://mlsanity.com/paper/2505.20977/) (2025)
- [A Systematic Review on Long-Tailed Learning](https://mlsanity.com/paper/2408.00483/) (2024)
- [Open Long-Tailed Recognition in a Dynamic World](https://mlsanity.com/paper/2208.08349/) (2022)
- [ConR: Contrastive Regularizer for Deep Imbalanced Regression](https://mlsanity.com/paper/2309.06651/) (2023)
- [Regression-based Deep-Learning predicts molecular biomarkers from pathology slides](https://mlsanity.com/paper/2304.05153/) (2023)
- [A step towards understanding why classification helps regression](https://mlsanity.com/paper/2308.10603/) (2023)
- [Semi-Supervised Graph Imbalanced Regression](https://mlsanity.com/paper/2305.12087/) (2023)
- [mCL-NER: Cross-Lingual Named Entity Recognition via Multi-view Contrastive Learning](https://mlsanity.com/paper/2308.09073/) (2023)
- [E2AT: Multimodal Jailbreak Defense via Dynamic Joint Optimization for Multimodal Large Language Models](https://mlsanity.com/paper/2503.04833/) (2025)
- [Convergence Rate Analysis of LION](https://mlsanity.com/paper/2411.07724/) (2024)
- [Taming Anomalies with Down-Up Sampling Networks: Group Center Preserving Reconstruction for 3D Anomaly Detection](https://mlsanity.com/paper/2507.03903/) (2025)
- [Deep Imbalanced Regression via Hierarchical Classification Adjustment](https://mlsanity.com/paper/2310.17154/) (2023)
- [Logit Normalization for Long-tail Object Detection](https://mlsanity.com/paper/2203.17020/) (2022)
- [Rebalanced Zero-shot Learning](https://mlsanity.com/paper/2210.07031/) (2022)
- [IM-Context: In-Context Learning for Imbalanced Regression Tasks](https://mlsanity.com/paper/2405.18202/) (2024)
- [Improve Representation for Imbalanced Regression through Geometric Constraints](https://mlsanity.com/paper/2503.00876/) (2025)
- [KBody: Towards general, robust, and aligned monocular whole-body estimation](https://mlsanity.com/paper/2304.11542/) (2023)
- [Data Optimization in Deep Learning: A Survey](https://mlsanity.com/paper/2310.16499/) (2023)
- [Data Augmentation with Variational Autoencoder for Imbalanced Dataset](https://mlsanity.com/paper/2412.07039/) (2024)
- [Dual Graph Multitask Framework for Imbalanced Delivery Time Estimation](https://mlsanity.com/paper/2302.07429/) (2023)
- [Rethinking Class Imbalance in Machine Learning](https://mlsanity.com/paper/2305.03900/) (2023)
- [Uncertainty Voting Ensemble for Imbalanced Deep Regression](https://mlsanity.com/paper/2305.15178/) (2023)
- [Score-balanced Loss for Multi-aspect Pronunciation Assessment](https://mlsanity.com/paper/2305.16664/) (2023)
- [Generalized Oversampling for Learning from Imbalanced datasets and Associated Theory](https://mlsanity.com/paper/2308.02966/) (2023)
- [Long-tailed Recognition by Learning from Latent Categories](https://mlsanity.com/paper/2206.01010/) (2022)
- [Dist Loss: Enhancing Regression in Few-Shot Region through Distribution Distance Constraint](https://mlsanity.com/paper/2411.15216/) (2024)
- [Local distribution-based adaptive oversampling for imbalanced regression](https://mlsanity.com/paper/2504.14316/) (2025)
- [IMG: Calibrating Diffusion Models via Implicit Multimodal Guidance](https://mlsanity.com/paper/2509.26231/) (2025)

## Abstract (arXiv)

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.