Random spanning trees and the prediction of weighted graphs
Nicolò Cesa-Bianchi, Claudio Gentile, Fabio Vitale and Giovanni Zappella
In: ICML 2010, Haifa, Israel(2010).
We show that the mistake bound for predicting the nodes of an arbitrary weighted graph is 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 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.