Fast and Optimal Algorithms for Weighted Graph Prediction

We 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 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. Preliminary experiments on real-world datasets show that our method outperforms both global (Perceptron) and local (majority voting) methods.