## AbstractWe show that the mistake bound for predicting the nodes of an arbitrary weighted graph is characterized (up to logarithmic factors) by the weighted cutsize of a random spanning tree of the graph. The cutsize is induced by the unknown adversarial labeling of the graph nodes. In deriving our characterization, we obtain a simple randomized algorithm achieving the optimal mistake bound on any weighted graph. Our algorithm draws a random spanning tree of the original graph and then predicts the nodes of this tree in constant amortized time and linear space. Experiments on real-world datasets show that our method compares well to both global (Perceptron) and local (label-propagation) methods, while being much faster.
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