Gaussian Process Classification with Privileged Information by Soft-to-Hard Labeling Transfer

Abstract: Learning using privileged information is an attractive problem setting that helps many learning scenarios in the real world. A state-of-the-art method of Gaussian process classification (GPC) with privileged information is GPC+, which incorporates privileged information into a noise term of the likelihood. A drawback of GPC+ is that it requires numerical quadrature to calculate the posterior distribution of the latent function, which is extremely time-consuming. To overcome this limitation, we propose a novel classification method with privileged information based on Gaussian processes, called "soft-label-transferred Gaussian process (SLT-GP)." Our basic idea is that we construct another learning task of predicting soft labels (continuous values) obtained from privileged information and we perform transfer learning from this task to the target task of predicting hard labels. We derive a PAC-Bayesian bound of our proposed method, which justifies optimizing hyperparameters by the empirical Bayes method. We also experimentally show the usefulness of our proposed method compared with GPC and GPC+.