  Semi-supervised learning algorithms attempt to take advantage of relatively
inexpensive unlabeled data to improve learning performance. In this work, we
consider statistical models where the data distributions can be characterized
by continuous parameters. We show that under certain conditions on the
distribution, unlabeled data is equally useful as labeled date in terms of
learning rate. Specifically, let $n, m$ be the number of labeled and unlabeled
data, respectively. It is shown that the learning rate of semi-supervised
learning 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 of
supervised learning scales as $O(1/n)$.
