# Semi-Supervised Learning, Causality and the Conditional Cluster Assumption

arXiv: https://arxiv.org/abs/1905.12081 · HTML: https://mlsanity.com/paper/1905.12081/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 May 2019.

## Built on by (most cited first, 15 of 15)

- [Towards Causal Representation Learning](https://mlsanity.com/paper/2102.11107/) (2021)
- [Independent mechanism analysis, a new concept?](https://mlsanity.com/paper/2106.05200/) (2021)
- [Nonlinear Invariant Risk Minimization: A Causal Approach](https://mlsanity.com/paper/2102.12353/) (2021)
- [From Statistical to Causal Learning](https://mlsanity.com/paper/2204.00607/) (2022)
- [Causal Direction of Data Collection Matters: Implications of Causal and Anticausal Learning for NLP](https://mlsanity.com/paper/2110.03618/) (2021)
- [Spuriosity Didn't Kill the Classifier: Using Invariant Predictions to Harness Spurious Features](https://mlsanity.com/paper/2307.09933/) (2023)
- [Detecting hidden confounding in observational data using multiple environments](https://mlsanity.com/paper/2205.13935/) (2022)
- [Identifiable Causal Representation Learning: Unsupervised, Multi-View, and Multi-Environment](https://mlsanity.com/paper/2406.13371/) (2024)
- [On Non-Random Missing Labels in Semi-Supervised Learning](https://mlsanity.com/paper/2206.14923/) (2022)
- [Revisiting Deep Semi-supervised Learning: An Empirical Distribution Alignment Framework and Its Generalization Bound](https://mlsanity.com/paper/2203.06639/) (2022)
- [New Rules for Causal Identification with Background Knowledge](https://mlsanity.com/paper/2407.15259/) (2024)
- [A Unifying Framework for Unsupervised Concept Extraction](https://mlsanity.com/paper/2604.24936/) (2026)
- [On the Role of Priors in Bayesian Causal Learning](https://mlsanity.com/paper/2504.01424/) (2025)
- [Mitigating Context Bias in Domain Adaptation for Object Detection using Mask Pooling](https://mlsanity.com/paper/2505.18446/) (2025)
- [Semi-Supervised Learning under General Causal Models](https://mlsanity.com/paper/2510.22567/) (2025)

## Abstract (arXiv)

While the success of semi-supervised learning (SSL) is still not fully understood, Sch"olkopf et al. (2012) have established a link to the principle of independent causal mechanisms. They conclude that SSL should be impossible when predicting a target variable from its causes, but possible when predicting it from its effects. Since both these cases are somewhat restrictive, we extend their work by considering classification using cause and effect features at the same time, such as predicting disease from both risk factors and symptoms. While standard SSL exploits information contained in the marginal distribution of all inputs (to improve the estimate of the conditional distribution of the target given inputs), we argue that in our more general setting we should use information in the conditional distribution of effect features given causal features. We explore how this insight generalises the previous understanding, and how it relates to and can be exploited algorithmically for SSL.