  Semi-Supervised Learning (SSL) under class distribution mismatch aims to
tackle a challenging problem wherein unlabeled data contain lots of unknown
categories unseen in the labeled ones. In such mismatch scenarios, traditional
SSL suffers severe performance damage due to the harmful invasion of the
instances with unknown categories into the target classifier. In this study, by
strict mathematical reasoning, we reveal that the SSL error under class
distribution mismatch is composed of pseudo-labeling error and invasion error,
both of which jointly bound the SSL population risk. To alleviate the SSL
error, we propose a robust SSL framework called Weight-Aware Distillation (WAD)
that, by weights, selectively transfers knowledge beneficial to the target task
from unsupervised contrastive representation to the target classifier.
Specifically, WAD captures adaptive weights and high-quality pseudo labels to
target instances by exploring point mutual information (PMI) in representation
space to maximize the role of unlabeled data and filter unknown categories.
Theoretically, we prove that WAD has a tight upper bound of population risk
under class distribution mismatch. Experimentally, extensive results
demonstrate that WAD outperforms five state-of-the-art SSL approaches and one
standard baseline on two benchmark datasets, CIFAR10 and CIFAR100, and an
artificial cross-dataset. The code is available at
https://github.com/RUC-DWBI-ML/research/tree/main/WAD-master.
