# Bayesian Pseudo Labels: Expectation Maximization for Robust and Efficient Semi-Supervised Segmentation

arXiv: https://arxiv.org/abs/2208.04435 · HTML: https://mlsanity.com/paper/2208.04435/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 29 references that are in the map.
- First posted on arXiv 8 Aug 2022.

## Builds on (most cited first, 20 of 20)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (2017)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [V-Net: Fully Convolutional Neural Networks for Volumetric Medical Image Segmentation](https://mlsanity.com/paper/1606.04797/) (2016)
- [RandAugment: Practical automated data augmentation with a reduced search space](https://mlsanity.com/paper/1909.13719/) (2019)
- [FixMatch: Simplifying Semi-Supervised Learning with Consistency and Confidence](https://mlsanity.com/paper/2001.07685/) (2020)
- [Adversarial examples in the physical world](https://mlsanity.com/paper/1607.02533/) (2016)
- [MixMatch: A Holistic Approach to Semi-Supervised Learning](https://mlsanity.com/paper/1905.02249/) (2019)
- [Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift](https://mlsanity.com/paper/1906.02530/) (2019)
- [Mean teachers are better role models: Weight-averaged consistency targets improve semi-supervised deep learning results](https://mlsanity.com/paper/1703.01780/) (2017)
- [Semi-Supervised Semantic Segmentation with Cross Pseudo Supervision](https://mlsanity.com/paper/2106.01226/) (2021)
- [Semi-Supervised Semantic Segmentation with Cross-Consistency Training](https://mlsanity.com/paper/2003.09005/) (2020)
- [ReMixMatch: Semi-Supervised Learning with Distribution Alignment and Augmentation Anchoring](https://mlsanity.com/paper/1911.09785/) (2019)
- [Semi-supervised Left Atrium Segmentation with Mutual Consistency Training](https://mlsanity.com/paper/2103.02911/) (2021)
- [Self-Loop Uncertainty: A Novel Pseudo-Label for Semi-Supervised Medical Image Segmentation](https://mlsanity.com/paper/2007.09854/) (2020)
- [Semi-Supervised Segmentation of Radiation-Induced Pulmonary Fibrosis from Lung CT Scans with Multi-Scale Guided Dense Attention](https://mlsanity.com/paper/2109.14172/) (2021)
- [Learning Morphological Feature Perturbations for Calibrated Semi-Supervised Segmentation](https://mlsanity.com/paper/2203.10196/) (2022)

## Built on by (most cited first, 5 of 5)

- [Learning Cross-view Visual Geo-localization without Ground Truth](https://mlsanity.com/paper/2403.12702/) (2024)
- [Striving for Simplicity: Simple Yet Effective Prior-Aware Pseudo-Labeling for Semi-Supervised Ultrasound Image Segmentation](https://mlsanity.com/paper/2503.13987/) (2025)
- [Expectation Maximization Pseudo Labels](https://mlsanity.com/paper/2305.01747/) (2023)
- [In-Context Ensemble Learning from Pseudo Labels Improves Video-Language Models for Low-Level Workflow Understanding](https://mlsanity.com/paper/2409.15867/) (2024)
- [REASON: Probability map-guided dual-branch fusion framework for gastric content assessment](https://mlsanity.com/paper/2511.01302/) (2025)

## Abstract (arXiv)

This paper concerns pseudo labelling in segmentation. Our contribution is fourfold. Firstly, we present a new formulation of pseudo-labelling as an Expectation-Maximization (EM) algorithm for clear statistical interpretation. Secondly, we propose a semi-supervised medical image segmentation method purely based on the original pseudo labelling, namely SegPL. We demonstrate SegPL is a competitive approach against state-of-the-art consistency regularisation based methods on semi-supervised segmentation on a 2D multi-class MRI brain tumour segmentation task and a 3D binary CT lung vessel segmentation task. The simplicity of SegPL allows less computational cost comparing to prior methods. Thirdly, we demonstrate that the effectiveness of SegPL may originate from its robustness against out-of-distribution noises and adversarial attacks. Lastly, under the EM framework, we introduce a probabilistic generalisation of SegPL via variational inference, which learns a dynamic threshold for pseudo labelling during the training. We show that SegPL with variational inference can perform uncertainty estimation on par with the gold-standard method Deep Ensemble.