We study the offline active learning problem on graphs. In this problem, one seeks to select k vertices whose labels are best suited for predicting the labels of all the other vertices in the graph.Guillory and Bilmes (Guillory & Bilmes, 2009) introduced a natural theoretical model motivated by a label smoothness assumption. Prior to our work, algorithms with theoretical guarantees were only known for restricted graph types such as trees (Cesa-Bianchi et al., 2010) despite the models simplicity. We present the first O(log n)-resource augmented algorithm for general weighted graphs. To complement our algorithm, we show constant hardness of approximation.

In active learning, you get to choose which data points are labeled. A real world example are surveys, where respondents are usually carefully picked rather than selected arbitrarily. We give a new algorithm for selecting which data points to label based on similarity information between data points. For a natural objective, our algorithm always performs at least as well as the optimal algorithm with a more limited budget, and we observe that it outperforms previous algorithms in experiments.