Random Spanning Trees and the Prediction of Weighted Graphs

  • Cesa-Bianchi N
  • Gentile C
  • Vitale F
 et al. 
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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 datasets show that our method compares well to both global (Perceptron) and local (label propagation) methods, while being generally faster in practice.

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Authors

  • Nicolo' Cesa-Bianchi

  • Claudio Gentile

  • Fabio Vitale

  • Giovanni Zappella

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