# Expectation Maximization Pseudo Labels

arXiv: https://arxiv.org/abs/2305.01747 · HTML: https://mlsanity.com/paper/2305.01747/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 55 references that are in the map.
- First posted on arXiv 2 May 2023.

## Builds on (most cited first, 30 of 39)

- [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)
- [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)
- [The Medical Segmentation Decathlon](https://mlsanity.com/paper/2106.05735/) (2021)
- [FedBN: Federated Learning on Non-IID Features via Local Batch Normalization](https://mlsanity.com/paper/2102.07623/) (2021)
- [Identifying the Best Machine Learning Algorithms for Brain Tumor Segmentation, Progression Assessment, and Overall Survival Prediction in the BRATS Challenge](https://mlsanity.com/paper/1811.02629/) (2018)
- [Pseudo-Labeling and Confirmation Bias in Deep Semi-Supervised Learning](https://mlsanity.com/paper/1908.02983/) (2019)
- [Semi-Supervised Semantic Segmentation with Cross Pseudo Supervision](https://mlsanity.com/paper/2106.01226/) (2021)
- [Uncertainty-aware Self-ensembling Model for Semi-supervised 3D Left Atrium Segmentation](https://mlsanity.com/paper/1907.07034/) (2019)
- [Semi-Supervised Semantic Segmentation with Cross-Consistency Training](https://mlsanity.com/paper/2003.09005/) (2020)
- [Meta Pseudo Labels](https://mlsanity.com/paper/2003.10580/) (2020)
- [ReMixMatch: Semi-Supervised Learning with Distribution Alignment and Augmentation Anchoring](https://mlsanity.com/paper/1911.09785/) (2019)
- [In Defense of Pseudo-Labeling: An Uncertainty-Aware Pseudo-label Selection Framework for Semi-Supervised Learning](https://mlsanity.com/paper/2101.06329/) (2021)
- [PseudoSeg: Designing Pseudo Labels for Semantic Segmentation](https://mlsanity.com/paper/2010.09713/) (2020)
- [Mutual Consistency Learning for Semi-supervised Medical Image Segmentation](https://mlsanity.com/paper/2109.09960/) (2021)
- [Semi-supervised Left Atrium Segmentation with Mutual Consistency Training](https://mlsanity.com/paper/2103.02911/) (2021)
- [Semi-Supervised Medical Image Segmentation via Cross Teaching between CNN and Transformer](https://mlsanity.com/paper/2112.04894/) (2021)
- [SimCVD: Simple Contrastive Voxel-Wise Representation Distillation for Semi-Supervised Medical Image Segmentation](https://mlsanity.com/paper/2108.06227/) (2021)
- [Semi-supervised Skin Lesion Segmentation via Transformation Consistent Self-ensembling Model](https://mlsanity.com/paper/1808.03887/) (2018)
- [Realistic Adversarial Data Augmentation for MR Image Segmentation](https://mlsanity.com/paper/2006.13322/) (2020)
- [Self-Loop Uncertainty: A Novel Pseudo-Label for Semi-Supervised Medical Image Segmentation](https://mlsanity.com/paper/2007.09854/) (2020)
- [Dual-Teacher: Integrating Intra-domain and Inter-domain Teachers for Annotation-efficient Cardiac Segmentation](https://mlsanity.com/paper/2007.06279/) (2020)

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

- [When and How Unlabeled Data Provably Improve In-Context Learning](https://mlsanity.com/paper/2506.15329/) (2025)
- [SEMF: Supervised Expectation-Maximization Framework for Predicting Intervals](https://mlsanity.com/paper/2405.18176/) (2024)

## Abstract (arXiv)

In this paper, we study pseudo-labelling. Pseudo-labelling employs raw inferences on unlabelled data as pseudo-labels for self-training. We elucidate the empirical successes of pseudo-labelling by establishing a link between this technique and the Expectation Maximisation algorithm. Through this, we realise that the original pseudo-labelling serves as an empirical estimation of its more comprehensive underlying formulation. Following this insight, we present a full generalisation of pseudo-labels under Bayes' theorem, termed Bayesian Pseudo Labels. Subsequently, we introduce a variational approach to generate these Bayesian Pseudo Labels, involving the learning of a threshold to automatically select high-quality pseudo labels. In the remainder of the paper, we showcase the applications of pseudo-labelling and its generalised form, Bayesian Pseudo-Labelling, in the semi-supervised segmentation of medical images. Specifically, we focus on: 1) 3D binary segmentation of lung vessels from CT volumes; 2) 2D multi-class segmentation of brain tumours from MRI volumes; 3) 3D binary segmentation of whole brain tumours from MRI volumes; and 4) 3D binary segmentation of prostate from MRI volumes. We further demonstrate that pseudo-labels can enhance the robustness of the learned representations. The code is released in the following GitHub repository: https://github.com/moucheng2017/EMSSL