A major challenge in Semi-Supervised Learning (SSL) is the limited information available about the class distribution in the unlabeled data. In many real-world applications this arises from the prevalence of long-tailed distributions, where the standard pseudo-label approach to SSL is biased towards the labeled class distribution and thus performs poorly on unlabeled data. Existing methods typically assume that the unlabeled class distribution is either known a priori, which is unrealistic in most situations, or estimate it on-the-fly using the pseudo-labels themselves. We propose to explicitly estimate the unlabeled class distribution, which is a finite-dimensional parameter, \emph{as an initial step}, using a doubly robust estimator with a strong theoretical guarantee; this estimate can then be integrated into existing methods to pseudo-label the unlabeled data during training more accurately. Experimental results demonstrate that incorporating our techniques into common pseudo-labeling approaches improves their performance.

Recent advancements in semi-supervised learning have focused on a more realistic yet challenging task: addressing imbalances in labeled data while the class distribution of unlabeled data remains both unknown and potentially mismatched. Current approaches in this sphere often presuppose rigid assumptions regarding the class distribution of unlabeled data, thereby limiting the adaptability of models to only certain distribution ranges. In this study, we propose a novel approach, introducing a highly adaptable framework, designated as SimPro, which does not rely on any predefined assumptions about the distribution of unlabeled data. Our framework, grounded in a probabilistic model, innovatively refines the expectation-maximization (EM) algorithm by explicitly decoupling the modeling of conditional and marginal class distributions. This separation facilitates a closed-form solution for class distribution estimation during the maximization phase, leading to the formulation of a Bayes classifier. The Bayes classifier, in turn, enhances the quality of pseudo-labels in the expectation phase. Remarkably, the SimPro framework not only comes with theoretical guarantees but also is straightforward to implement. Moreover, we introduce two novel class distributions broadening the scope of the evaluation. Our method showcases consistent state-of-the-art performance across diverse benchmarks and data distribution scenarios. Our code is available at https://github.com/LeapLabTHU/SimPro.