# SimPro: A Simple Probabilistic Framework Towards Realistic Long-Tailed Semi-Supervised Learning

arXiv: https://arxiv.org/abs/2402.13505 · HTML: https://mlsanity.com/paper/2402.13505/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 33 references that are in the map.
- First posted on arXiv 21 Feb 2024.

## Builds on (most cited first, 19 of 19)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [FixMatch: Simplifying Semi-Supervised Learning with Consistency and Confidence](https://mlsanity.com/paper/2001.07685/) (2020)
- [MixMatch: A Holistic Approach to Semi-Supervised Learning](https://mlsanity.com/paper/1905.02249/) (2019)
- [Virtual Adversarial Training: A Regularization Method for Supervised and Semi-Supervised Learning](https://mlsanity.com/paper/1704.03976/) (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)
- [Long-tail learning via logit adjustment](https://mlsanity.com/paper/2007.07314/) (2020)
- [Balanced Meta-Softmax for Long-Tailed Visual Recognition](https://mlsanity.com/paper/2007.10740/) (2020)
- [ReMixMatch: Semi-Supervised Learning with Distribution Alignment and Augmentation Anchoring](https://mlsanity.com/paper/1911.09785/) (2019)
- [CReST: A Class-Rebalancing Self-Training Framework for Imbalanced Semi-Supervised Learning](https://mlsanity.com/paper/2102.09559/) (2021)
- [Disentangling Label Distribution for Long-tailed Visual Recognition](https://mlsanity.com/paper/2012.00321/) (2020)
- [Distribution Aligning Refinery of Pseudo-label for Imbalanced Semi-supervised Learning](https://mlsanity.com/paper/2007.08844/) (2020)
- [ABC: Auxiliary Balanced Classifier for Class-imbalanced Semi-supervised Learning](https://mlsanity.com/paper/2110.10368/) (2021)
- [Nested Collaborative Learning for Long-Tailed Visual Recognition](https://mlsanity.com/paper/2203.15359/) (2022)
- [CoSSL: Co-Learning of Representation and Classifier for Imbalanced Semi-Supervised Learning](https://mlsanity.com/paper/2112.04564/) (2021)
- [Three Heads Are Better Than One: Complementary Experts for Long-Tailed Semi-supervised Learning](https://mlsanity.com/paper/2312.15702/) (2023)
- [Transfer and Share: Semi-Supervised Learning from Long-Tailed Data](https://mlsanity.com/paper/2205.13358/) (2022)

## Built on by (most cited first, 14 of 14)

- [A Systematic Review on Long-Tailed Learning](https://mlsanity.com/paper/2408.00483/) (2024)
- [Balancing the Scales: A Theoretical and Algorithmic Framework for Learning from Imbalanced Data](https://mlsanity.com/paper/2502.10381/) (2025)
- [Improved Balanced Classification with Theoretically Grounded Loss Functions](https://mlsanity.com/paper/2512.23947/) (2025)
- [A Square Peg in a Square Hole: Meta-Expert for Long-Tailed Semi-Supervised Learning](https://mlsanity.com/paper/2505.16341/) (2025)
- [UniTTA: Unified Benchmark and Versatile Framework Towards Realistic Test-Time Adaptation](https://mlsanity.com/paper/2407.20080/) (2024)
- [Optimized Deferral for Imbalanced Settings](https://mlsanity.com/paper/2604.27723/) (2026)
- [Decouple then Converge: Handling Unknown Unlabeled Distributions in Long-Tailed Semi-Supervised Learning](https://mlsanity.com/paper/2406.13187/) (2024)
- [BAPE: Learning an Explicit Bayes Classifier for Long-tailed Visual Recognition](https://mlsanity.com/paper/2506.23280/) (2025)
- [Keep It on a Leash: Controllable Pseudo-label Generation Towards Realistic Long-Tailed Semi-Supervised Learning](https://mlsanity.com/paper/2510.03993/) (2025)
- [Geometric Regularization for Long-Tailed Semi-Supervised Learning via Gaussian Feature Bridges](https://mlsanity.com/paper/2608.20710/) (2026)
- [Imbalanced Semi-Supervised Learning via Label Refinement and Threshold Adjustment](https://mlsanity.com/paper/2407.05370/) (2024)
- [FedHUG: Federated Heterogeneous Unsupervised Generalization for Remote Physiological Measurements](https://mlsanity.com/paper/2510.12132/) (2025)
- [Solving Semi-Supervised Few-Shot Learning from an Auto-Annotation Perspective](https://mlsanity.com/paper/2512.10244/) (2025)
- [Beyond Distribution Estimation: Simplex Anchored Structural Inference Towards Universal Semi-Supervised Learning](https://mlsanity.com/paper/2605.07557/) (2026)

## Abstract (arXiv)

Recent advancements in semi-supervised learning have focused on a more realistic yet challenging task: addressing imbalances in labeled data while the class distribution of unlabeled data remains both unknown and potentially mismatched. Current approaches in this sphere often presuppose rigid assumptions regarding the class distribution of unlabeled data, thereby limiting the adaptability of models to only certain distribution ranges. In this study, we propose a novel approach, introducing a highly adaptable framework, designated as SimPro, which does not rely on any predefined assumptions about the distribution of unlabeled data. Our framework, grounded in a probabilistic model, innovatively refines the expectation-maximization (EM) algorithm by explicitly decoupling the modeling of conditional and marginal class distributions. This separation facilitates a closed-form solution for class distribution estimation during the maximization phase, leading to the formulation of a Bayes classifier. The Bayes classifier, in turn, enhances the quality of pseudo-labels in the expectation phase. Remarkably, the SimPro framework not only comes with theoretical guarantees but also is straightforward to implement. Moreover, we introduce two novel class distributions broadening the scope of the evaluation. Our method showcases consistent state-of-the-art performance across diverse benchmarks and data distribution scenarios. Our code is available at https://github.com/LeapLabTHU/SimPro.