MTSSL: Meta-Thresholding Semi-Supervised Learning

A large body of Semi-supervised Learning~(SSL) algorithms encounter the threshold $τ$ to select pseudo-labels. The value of $τ$ across different SSL algorithms can vary depending on the learning perspective, yet they may achieve similar performance. It motivates us to establish a unified theoretical framework to explain the role of $τ$ in SSL. We statistically explained that the unsupervised loss is affected independently by correct and incorrect pseudo-labels, while $τ$ adjusts their numbers to balance the corresponding error term. This inherent trade-off indicates that SSL can reach the same loss with varying $τ$, precise optimal values of $τ$ during training may be unnecessary. With this, we treat $τ$ as an updatable parameter and optimize it via differentiation; the new policy is named \textbf{Meta-Thresholding Semi-Supervised Learning (MTSSL)}. Extensive experiments demonstrate the superior performance of MTSSL. We observe that the accuracy curves of SSL algorithms can overlap completely even when the values of $τ$ differ significantly, which supports our theoretical framework and indicates that the selection of $τ$ can be relaxed in the future design of SSL algorithms.

Probability-density-aware Semi-supervised Learning

Semi-supervised learning (SSL) assumes that neighbor points lie in the same category (neighbor assumption), and points in different clusters belong to various categories (cluster assumption). Existing methods usually rely on similarity measures to retrieve the similar neighbor points, ignoring cluster assumption, which may not utilize unlabeled information sufficiently and effectively. This paper first provides a systematical investigation into the significant role of probability density in SSL and lays a solid theoretical foundation for cluster assumption. To this end, we introduce a Probability-Density-Aware Measure (PM) to discern the similarity between neighbor points. To further improve Label Propagation, we also design a Probability-Density-Aware Measure Label Propagation (PMLP) algorithm to fully consider the cluster assumption in label propagation. Last but not least, we prove that traditional 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.