# Prior2Posterior: Model Prior Correction for Long-Tailed Learning

arXiv: https://arxiv.org/abs/2412.16540 · HTML: https://mlsanity.com/paper/2412.16540/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 50 references that are in the map.
- First posted on arXiv 21 Dec 2024.

## Builds on (most cited first, 30 of 31)

- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (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)
- [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)
- [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)
- [Long-Tailed Classification by Keeping the Good and Removing the Bad Momentum Causal Effect](https://mlsanity.com/paper/2009.12991/) (2020)
- [Improving Calibration for Long-Tailed Recognition](https://mlsanity.com/paper/2104.00466/) (2021)
- [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)
- [Seesaw Loss for Long-Tailed Instance Segmentation](https://mlsanity.com/paper/2008.10032/) (2020)
- [Balanced Contrastive Learning for Long-Tailed Visual Recognition](https://mlsanity.com/paper/2207.09052/) (2022)
- [Long-Tailed Recognition via Weight Balancing](https://mlsanity.com/paper/2203.14197/) (2022)
- [The Majority Can Help The Minority: Context-rich Minority Oversampling for Long-tailed Classification](https://mlsanity.com/paper/2112.00412/) (2021)
- [MetaSAug: Meta Semantic Augmentation for Long-Tailed Visual Recognition](https://mlsanity.com/paper/2103.12579/) (2021)
- [ResLT: Residual Learning for Long-tailed Recognition](https://mlsanity.com/paper/2101.10633/) (2021)
- [Distributional Robustness Loss for Long-tail Learning](https://mlsanity.com/paper/2104.03066/) (2021)
- [Long-tailed Visual Recognition via Gaussian Clouded Logit Adjustment](https://mlsanity.com/paper/2305.11733/) (2023)
- [RSG: A Simple but Effective Module for Learning Imbalanced Datasets](https://mlsanity.com/paper/2106.09859/) (2021)
- [Adaptive Class Suppression Loss for Long-Tail Object Detection](https://mlsanity.com/paper/2104.00885/) (2021)
- [Global and Local Mixture Consistency Cumulative Learning for Long-tailed Visual Recognitions](https://mlsanity.com/paper/2305.08661/) (2023)
- [SoLar: Sinkhorn Label Refinery for Imbalanced Partial-Label Learning](https://mlsanity.com/paper/2209.10365/) (2022)
- [Escaping Saddle Points for Effective Generalization on Class-Imbalanced Data](https://mlsanity.com/paper/2212.13827/) (2022)
- [Inducing Neural Collapse in Deep Long-tailed Learning](https://mlsanity.com/paper/2302.12453/) (2023)
- [Margin Calibration for Long-Tailed Visual Recognition](https://mlsanity.com/paper/2112.07225/) (2021)
- [Decoupled Training for Long-Tailed Classification With Stochastic Representations](https://mlsanity.com/paper/2304.09426/) (2023)

## Built on by (most cited first, 2 of 2)

- [Local Reference Geometry Residual Augmentation for Imbalanced Time Series Classification](https://mlsanity.com/paper/2609.00093/) (2026)
- [Learning under Localized Minority Imbalance](https://mlsanity.com/paper/2610.04936/) (2026)

## Abstract (arXiv)

Learning-based solutions for long-tailed recognition face difficulties in generalizing on balanced test datasets. Due to imbalanced data prior, the learned textita posteriori distribution is biased toward the most frequent (head) classes, leading to an inferior performance on the least frequent (tail) classes. In general, the performance can be improved by removing such a bias by eliminating the effect of imbalanced prior modeled using the number of class samples (frequencies). We first observe that the textiteffective prior on the classes, learned by the model at the end of the training, can differ from the empirical prior obtained using class frequencies. Thus, we propose a novel approach to accurately model the effective prior of a trained model using textita posteriori probabilities. We propose to correct the imbalanced prior by adjusting the predicted textita posteriori probabilities (Prior2Posterior: P2P) using the calculated prior in a post-hoc manner after the training, and show that it can result in improved model performance. We present theoretical analysis showing the optimality of our approach for models trained with naive cross-entropy loss as well as logit adjusted loss. Our experiments show that the proposed approach achieves new state-of-the-art (SOTA) on several benchmark datasets from the long-tail literature in the category of logit adjustment methods. Further, the proposed approach can be used to inspect any existing method to capture the textiteffective prior and remove any residual bias to improve its performance, post-hoc, without model retraining. We also show that by using the proposed post-hoc approach, the performance of many existing methods can be improved further.