Random spanning trees and the prediction of weighted graphs
Nicolò Cesa-Bianchi, Claudio Gentile, Fabio Vitale and Giovanni Zappella
In: ICML 2010, June 2010, Haifa, Israel.
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 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