These are shown to increase either the likelihood of the training data, or a lower bound on that likelihood.
abney defines a function K that is an upper bound on the negative log-likelihood, and shows his bootstrapping algorithms locally minimize K. We now present a generalization of abney's K function and relate it to another semi-supervised learning technique, entropy regularization (Brand, 1999;Grandvalet and Bengio, 2005;Jiao et al., 2006).