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Semi-supervised learning algorithms attempt to take advantage of relativelyinexpensive unlabeled data to improve learning performance. In this work, weconsider statistical models where the data distributions can be characterizedby continuous parameters. We show that under certain conditions on thedistribution, unlabeled data is equally useful as labeled date in terms oflearning rate. Specifically, let $n, m$ be the number of labeled and unlabeleddata, respectively. It is shown that the learning rate of semi-supervisedlearning scales as $O(1/n)$ if $m\sim n$, and scales as $O(1/n^{1+\gamma})$ if$m\sim n^{1+\gamma}$ for some $\gamma>0$, whereas the learning rate ofsupervised learning scales as $O(1/n)$.

Semi-Supervised Learning: the Case When Unlabeled Data is Equally Useful