Probability-Density-aware Semi-supervised Learning
Shuyang Liu, Ruiqiu Zheng, Yunhang Shen, Zhou Yu, Ke Li, Xing Sun, Shaohui Lin
Abstract
In Semi-supervised learning(SSL), we always accept cluster assumption, assuming features in different high-density regions belong to other categories. However, it is always ignored by existing algorithms and needs mathematical explanations. This paper first proposes a theorem to statistically explain cluster assumption and prove that the probability density can significantly help to use the prior fully. A Probability-Density-Aware Measure(PM) is proposed based on the theorem to discern the similarity between neighbor points. The PM is deployed to improve Label Propagation and a new pseudo-labeling algorithm, the Probability-Density-Aware Label Propagation(PMLP), is proposed. We also prove that traditional first-order similarity pseudo-labeling could be viewed as a particular case of PMLP, which provides a comprehensive theoretical understanding of PMLP's superior performance. Extensive experiments demonstrate that PMLP achieves outstanding performance compared with other recent methods.
BibTeX
@article{Liu_Zheng_Shen_Yu_Li_Sun_Lin_2025, title={Probability-Density-aware Semi-supervised Learning}, volume={39}, url={https://ojs.aaai.org/index.php/AAAI/article/view/34085}, DOI={10.1609/aaai.v39i18.34085}, abstractNote={In Semi-supervised learning(SSL), we always accept cluster assumption, assuming features in different high-density regions belong to other categories. However, it is always ignored by existing algorithms and needs mathematical explanations. This paper first proposes a theorem to statistically explain cluster assumption and prove that the probability density can significantly help to use the prior fully. A Probability-Density-Aware Measure(PM) is proposed based on the theorem to discern the similarity between neighbor points. The PM is deployed to improve Label Propagation and a new pseudo-labeling algorithm, the Probability-Density-Aware Label Propagation(PMLP), is proposed. We also prove that traditional first-order similarity pseudo-labeling could be viewed as a particular case of PMLP, which provides a comprehensive theoretical understanding of PMLP’s superior performance. Extensive experiments demonstrate that PMLP achieves outstanding performance compared with other recent methods.}, number={18}, journal={Proceedings of the AAAI Conference on Artificial Intelligence}, author={Liu, Shuyang and Zheng, Ruiqiu and Shen, Yunhang and Yu, Zhou and Li, Ke and Sun, Xing and Lin, Shaohui}, year={2025}, month={Apr.}, pages={18943-18950} }