Random spanning trees and the prediction ofweighted graphs

Authors:
Nicolò Cesa-Bianchi;Claudio Gentile;Fabio Vitale;Giovanni Zappella
Affiliations:
Dipartimento di Informatica, Università degli Studi di Milano, Milano, Italy;DiSTA, Università dell'Insubria, Varese, Italy;Dipartimento di Informatica, Università degli Studi di Milano, Milano, Italy;Dipartimento di Matematica, Università degli Studi di Milano, Milano, Italy
Venue:
The Journal of Machine Learning Research
Year:
2013

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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.