## AbstractActive learning algorithms for graph node classification select a subset $L$ of nodes in a given graph. The goal is to minimize the mistakes made on the remaining nodes by a standard node classifier using $L$ as training set. Bilmes and Guillory introduced a combinatorial quantity, $\Psi^*(L)$, and related it to the performance of the mincut classifier run on any given training set $L$. While no efficient algorithms for minimizing $\Psi^*$ are known, they show that simple heuristics for (approximately) minimizing it do not work well in practice. Building on previous theoretical results about active learning on trees, we show that exact minimization of $\Psi^*$ on suitable spanning trees of the graph yields an efficient active learner that compares well against standard baselines on real-world graphs.
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