Ashish Kapoor, Hyungil Ahn, Yuan Qi, Rosalind Picard
There have been many graph-based approaches for semi-supervised clas- siﬁcation. One problem is that of hyperparameter learning: performance depends greatly on the hyperparameters of the similarity graph, trans- formation of the graph Laplacian and the noise model. We present a Bayesian framework for learning hyperparameters for graph-based semi- supervised classiﬁcation. Given some labeled data, which can contain inaccurate labels, we pose the semi-supervised classiﬁcation as an in- ference problem over the unknown labels. Expectation Propagation is used for approximate inference and the mean of the posterior is used for classiﬁcation. The hyperparameters are learned using EM for evidence maximization. We also show that the posterior mean can be written in terms of the kernel matrix, providing a Bayesian classiﬁer to classify new points. Tests on synthetic and real datasets show cases where there are signiﬁcant improvements in performance over the existing approaches.