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# A Variance Minimization Criterion to Active Learning on Graphs

*Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics*, PMLR 22:556-564, 2012.

#### Abstract

We consider the problem of active learning over the vertices in a graph, without feature representation. Our study is based on the common graph smoothness assumption, which is formulated in a Gaussian random field model. We analyze the probability distribution over the unlabeled vertices conditioned on the label information, which is a multivariate normal with the mean being the harmonic solution over the field. Then we select the nodes to label such that the total variance of the distribution on the unlabeled data, as well as the expected prediction error, is minimized. In this way, the classifier we obtain is theoretically more robust. Compared with existing methods, our algorithm has the advantage of selecting data in a batch offline mode with solid theoretical support. We show improved performance over existing label selection criteria on several real world data sets.