Hyperparameter and Kernel Learning for Graph Based Semi-Supervised Classification

There have been many graph-based approaches for semi-supervised classification. Oneproblem is that of hyperparameter learning: performance depends greatly on the hyperparameters of the similarity graph, transformation ofthe graph Laplacian and the noise model. We present a Bayesian framework for learning hyperparameters for graph-based semisupervised classification.Given some labeled data, which can contain inaccurate labels, we pose the semi-supervised classification as an inference problemover 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.