# Random Spanning Trees and the Prediction of Weighted Graphs

NicolĂ˛ Cesa-Bianchi, Claudio Gentile, Fabio Vitale, Giovanni Zappella.

Year: 2013, Volume: 14, Issue: 2, Pages: 1251−1284

#### Abstract

We investigate the problem of sequentially predicting the binary labels on the nodes of an arbitrary weighted graph. We show that, under a suitable parametrization of the problem, the optimal number of prediction mistakes can be characterized (up to logarithmic factors) by the 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 in expectation the optimal mistake bound on any polynomially connected weighted graph. Our algorithm draws a random spanning tree of the original graph and then predicts the nodes of this tree in constant expected amortized time and linear space. Experiments on real-world data sets show that our method compares well to both global (Perceptron) and local (label propagation) methods, while being generally faster in practice.