# Cross-Domain Empirical Risk Minimization for Unbiased Long-tailed Classification

arXiv: https://arxiv.org/abs/2112.14380 · HTML: https://mlsanity.com/paper/2112.14380/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 45 references that are in the map.
- First posted on arXiv 29 Dec 2021.

## Builds on (most cited first, 30 of 33)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Aggregated Residual Transformations for Deep Neural Networks](https://mlsanity.com/paper/1611.05431/) (2016)
- [Learning Deep Features for Discriminative Localization](https://mlsanity.com/paper/1512.04150/) (2015)
- [Class-Balanced Loss Based on Effective Number of Samples](https://mlsanity.com/paper/1901.05555/) (2019)
- [Learning Imbalanced Datasets with Label-Distribution-Aware Margin Loss](https://mlsanity.com/paper/1906.07413/) (2019)
- [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)
- [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)
- [Be Your Own Teacher: Improve the Performance of Convolutional Neural Networks via Self Distillation](https://mlsanity.com/paper/1905.08094/) (2019)
- [BBN: Bilateral-Branch Network with Cumulative Learning for Long-Tailed Visual Recognition](https://mlsanity.com/paper/1912.02413/) (2019)
- [Equalization Loss for Long-Tailed Object Recognition](https://mlsanity.com/paper/2003.05176/) (2020)
- [Long-tailed Recognition by Routing Diverse Distribution-Aware Experts](https://mlsanity.com/paper/2010.01809/) (2020)
- [Counterfactual VQA: A Cause-Effect Look at Language Bias](https://mlsanity.com/paper/2006.04315/) (2020)
- [Long-Tailed Classification by Keeping the Good and Removing the Bad Momentum Causal Effect](https://mlsanity.com/paper/2009.12991/) (2020)
- [Distribution Alignment: A Unified Framework for Long-tail Visual Recognition](https://mlsanity.com/paper/2103.16370/) (2021)
- [Learning From Multiple Experts: Self-paced Knowledge Distillation for Long-tailed Classification](https://mlsanity.com/paper/2001.01536/) (2020)
- [Disentangling Label Distribution for Long-tailed Visual Recognition](https://mlsanity.com/paper/2012.00321/) (2020)
- [Cost Sensitive Learning of Deep Feature Representations from Imbalanced Data](https://mlsanity.com/paper/1508.03422/) (2015)
- [Counterfactual Samples Synthesizing for Robust Visual Question Answering](https://mlsanity.com/paper/2003.06576/) (2020)
- [Learning from Failure: Training Debiased Classifier from Biased Classifier](https://mlsanity.com/paper/2007.02561/) (2020)
- [Deep Representation Learning on Long-tailed Data: A Learnable Embedding Augmentation Perspective](https://mlsanity.com/paper/2002.10826/) (2020)
- [Relay Backpropagation for Effective Learning of Deep Convolutional Neural Networks](https://mlsanity.com/paper/1512.05830/) (2015)
- [Causal Attention for Vision-Language Tasks](https://mlsanity.com/paper/2103.03493/) (2021)
- [Counterfactual Zero-Shot and Open-Set Visual Recognition](https://mlsanity.com/paper/2103.00887/) (2021)
- [Two Causal Principles for Improving Visual Dialog](https://mlsanity.com/paper/1911.10496/) (2019)
- [Distilling Virtual Examples for Long-tailed Recognition](https://mlsanity.com/paper/2103.15042/) (2021)
- [Deconfounded Image Captioning: A Causal Retrospect](https://mlsanity.com/paper/2003.03923/) (2020)
- [Deep Imbalanced Attribute Classification using Visual Attention Aggregation](https://mlsanity.com/paper/1807.03903/) (2018)
- [Class-Balanced Distillation for Long-Tailed Visual Recognition](https://mlsanity.com/paper/2104.05279/) (2021)

## Built on by (most cited first, 19 of 19)

- [Prompt-aligned Gradient for Prompt Tuning](https://mlsanity.com/paper/2205.14865/) (2022)
- [Probabilistic Contrastive Learning for Long-Tailed Visual Recognition](https://mlsanity.com/paper/2403.06726/) (2024)
- [Invariant Feature Learning for Generalized Long-Tailed Classification](https://mlsanity.com/paper/2207.09504/) (2022)
- [Enhancing Zero-Shot Vision Models by Label-Free Prompt Distribution Learning and Bias Correcting](https://mlsanity.com/paper/2410.19294/) (2024)
- [DiGeo: Discriminative Geometry-Aware Learning for Generalized Few-Shot Object Detection](https://mlsanity.com/paper/2303.09674/) (2023)
- [Label-Noise Learning with Intrinsically Long-Tailed Data](https://mlsanity.com/paper/2208.09833/) (2022)
- [Towards Calibrated Hyper-Sphere Representation via Distribution Overlap Coefficient for Long-tailed Learning](https://mlsanity.com/paper/2208.10043/) (2022)
- [NCL++: Nested Collaborative Learning for Long-Tailed Visual Recognition](https://mlsanity.com/paper/2306.16709/) (2023)
- [Transfer and Share: Semi-Supervised Learning from Long-Tailed Data](https://mlsanity.com/paper/2205.13358/) (2022)
- [DELTA: Decoupling Long-Tailed Online Continual Learning](https://mlsanity.com/paper/2404.04476/) (2024)
- [Counterfactual Multihop QA: A Cause-Effect Approach for Reducing Disconnected Reasoning](https://mlsanity.com/paper/2210.07138/) (2022)
- [Long-Tailed Learning as Multi-Objective Optimization](https://mlsanity.com/paper/2310.20490/) (2023)
- [Minority-Oriented Vicinity Expansion with Attentive Aggregation for Video Long-Tailed Recognition](https://mlsanity.com/paper/2211.13471/) (2022)
- [Empowering Vision Transformers with Multi-Scale Causal Intervention for Long-Tailed Image Classification](https://mlsanity.com/paper/2505.08173/) (2025)
- [EiHi Net: Out-of-Distribution Generalization Paradigm](https://mlsanity.com/paper/2209.14946/) (2022)
- [Predicate Debiasing in Vision-Language Models Integration for Scene Graph Generation Enhancement](https://mlsanity.com/paper/2403.16184/) (2024)
- [Decouple then Converge: Handling Unknown Unlabeled Distributions in Long-Tailed Semi-Supervised Learning](https://mlsanity.com/paper/2406.13187/) (2024)
- [Long-Tailed Classification Based on Coarse-Grained Leading Forest and Multi-Center Loss](https://mlsanity.com/paper/2310.08206/) (2023)
- [Normalizing Batch Normalization for Long-Tailed Recognition](https://mlsanity.com/paper/2501.03122/) (2025)

## Abstract (arXiv)

We address the overlooked unbiasedness in existing long-tailed classification methods: we find that their overall improvement is mostly attributed to the biased preference of tail over head, as the test distribution is assumed to be balanced; however, when the test is as imbalanced as the long-tailed training data -- let the test respect Zipf's law of nature -- the tail bias is no longer beneficial overall because it hurts the head majorities. In this paper, we propose Cross-Domain Empirical Risk Minimization (xERM) for training an unbiased model to achieve strong performances on both test distributions, which empirically demonstrates that xERM fundamentally improves the classification by learning better feature representation rather than the head vs. tail game. Based on causality, we further theoretically explain why xERM achieves unbiasedness: the bias caused by the domain selection is removed by adjusting the empirical risks on the imbalanced domain and the balanced but unseen domain. Codes are available at https://github.com/BeierZhu/xERM.