Reducing the Unlabeled Sample Complexity of Semi-Supervised Multi-view Learning

In semi-supervised multi-view learning, unlabeled sample complexity (u.s.c.) specifies the size of unlabeled training sample that guarantees a desired learning error. In this paper, we improve the state-of-art u.s.c. from O(1/epsilon) to O(log 1/epsilon) for small error epsilon, under mild conditions. To obtain the improved result, as a primary step we prove a connection between the generalization error of a classifier and its incompatibility, which measures the fitness between the classifier and the sample distribution. We then prove that with a sufficiently large unlabeled sample, one is able to find classifiers with low incompatibility. Combining the two observations, we manage to prove a probably approximately correct (PAC) style learning bound for semi-supervised multi-view learning. We empirically verified our theory by designing two proof-of concept algorithms, one based on active view sensing and the other based on online co-regularization, with real-world data sets.