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We currently do not have an understanding of semi-supervised learning (SSL)objectives such as pseudo-labelling and entropy minimization aslog-likelihoods, which precludes the development of e.g. Bayesian SSL. Here, wenote that benchmark image datasets such as CIFAR-10 are carefully curated, andwe formulate SSL objectives as a log-likelihood in a generative model of datacuration that was initially developed to explain the cold-posterior effect(Aitchison 2020). SSL methods, from entropy minimization and pseudo-labelling,to state-of-the-art techniques similar to FixMatch can be understood aslower-bounds on our principled log-likelihood. We are thus able to give aproof-of-principle for Bayesian SSL on toy data. Finally, our theory suggeststhat SSL is effective in part due to the statistical patterns induced by datacuration. This provides an explanation of past results which show SSL performsbetter on clean datasets without any "out of distribution" examples. Confirmingthese results we find that SSL gave much larger performance improvements oncurated than on uncurated data, using matched curated and uncurated datasetsbased on Galaxy Zoo 2.

Semi-supervised learning objectives as log-likelihoods in a generative model of data curation