  Using information-theoretic principles, we consider the generalization error
(gen-error) of iterative semi-supervised learning (SSL) algorithms that
iteratively generate pseudo-labels for a large amount of unlabelled data to
progressively refine the model parameters. In contrast to most previous works
that {\em bound} the gen-error, we provide an {\em exact} expression for the
gen-error and particularize it to the binary Gaussian mixture model. Our
theoretical results suggest that when the class conditional variances are not
too large, the gen-error decreases with the number of iterations, but quickly
saturates. On the flip side, if the class conditional variances (and so amount
of overlap between the classes) are large, the gen-error increases with the
number of iterations. To mitigate this undesirable effect, we show that
regularization can reduce the gen-error. The theoretical results are
corroborated by extensive experiments on the MNIST and CIFAR datasets in which
we notice that for easy-to-distinguish classes, the gen-error improves after
several pseudo-labelling iterations, but saturates afterwards, and for more
difficult-to-distinguish classes, regularization improves the generalization
performance.
