# BAPE: Learning an Explicit Bayes Classifier for Long-tailed Visual Recognition

arXiv: https://arxiv.org/abs/2506.23280 · HTML: https://mlsanity.com/paper/2506.23280/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 50 of its 73 references that are in the map.
- First posted on arXiv 29 Jun 2025.

## Builds on (most cited first, 30 of 50)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Aggregated Residual Transformations for Deep Neural Networks](https://mlsanity.com/paper/1611.05431/) (2016)
- [RandAugment: Practical automated data augmentation with a reduced search space](https://mlsanity.com/paper/1909.13719/) (2019)
- [Improved Regularization of Convolutional Neural Networks with Cutout](https://mlsanity.com/paper/1708.04552/) (2017)
- [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)
- [CosFace: Large Margin Cosine Loss for Deep Face Recognition](https://mlsanity.com/paper/1801.09414/) (2018)
- [Decoupling Representation and Classifier for Long-Tailed Recognition](https://mlsanity.com/paper/1910.09217/) (2019)
- [Long-tail learning via logit adjustment](https://mlsanity.com/paper/2007.07314/) (2020)
- [Exploring the Limits of Weakly Supervised Pretraining](https://mlsanity.com/paper/1805.00932/) (2018)
- [A systematic study of the class imbalance problem in convolutional neural networks](https://mlsanity.com/paper/1710.05381/) (2017)
- [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)
- [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)
- [Long-Tailed Classification by Keeping the Good and Removing the Bad Momentum Causal Effect](https://mlsanity.com/paper/2009.12991/) (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)
- [Distribution Alignment: A Unified Framework for Long-tail Visual Recognition](https://mlsanity.com/paper/2103.16370/) (2021)
- [Disentangling Label Distribution for Long-tailed Visual Recognition](https://mlsanity.com/paper/2012.00321/) (2020)
- [Exploring Deep Neural Networks via Layer-Peeled Model: Minority Collapse in Imbalanced Training](https://mlsanity.com/paper/2101.12699/) (2021)
- [Seesaw Loss for Long-Tailed Instance Segmentation](https://mlsanity.com/paper/2008.10032/) (2020)
- [Targeted Supervised Contrastive Learning for Long-Tailed Recognition](https://mlsanity.com/paper/2111.13998/) (2021)
- [Distribution-Balanced Loss for Multi-Label Classification in Long-Tailed Datasets](https://mlsanity.com/paper/2007.09654/) (2020)

## Built on by (most cited first, 1 of 1)

- [Does a Shared Temperature Imply a Shared Angular Scale in Probabilistic Contrastive Learning?](https://mlsanity.com/paper/2609.38784/) (2026)

## Abstract (arXiv)

Bayesian decision theory advocates the Bayes classifier as the optimal approach for minimizing the risk in machine learning problems. Current deep learning algorithms usually solve for the optimal classifier by implicitly estimating the posterior probabilities, e.g., by minimizing the Softmax cross-entropy loss. This simple methodology has been proven effective for meticulously balanced academic benchmark datasets. However, it is not applicable to the long-tailed data distributions in the real world, where it leads to the gradient imbalance issue and fails to ensure the Bayes optimal decision rule. To address these challenges, this paper presents a novel approach (BAPE) that provides a more precise theoretical estimation of the data distributions by explicitly modeling the parameters of the posterior probabilities and solving them with point estimation. Consequently, our method directly learns the Bayes classifier without gradient descent based on Bayes' theorem, simultaneously alleviating the gradient imbalance and ensuring the Bayes optimal decision rule. Furthermore, we propose a straightforward yet effective distribution adjustment technique. This method enables the Bayes classifier trained from the long-tailed training set to effectively adapt to the test data distribution with an arbitrary imbalance factor, thereby enhancing performance without incurring additional computational costs. In addition, we demonstrate the gains of our method are orthogonal to existing learning approaches for long-tailed scenarios, as they are mostly designed under the principle of implicitly estimating the posterior probabilities. Extensive empirical evaluations on CIFAR-10-LT, CIFAR-100-LT, ImageNet-LT, and iNaturalist demonstrate that our method significantly improves the generalization performance of popular deep networks, despite its simplicity.