Random Spanning Trees and the Prediction of Weighted Graphs

TL;DR

This paper introduces a randomized algorithm for predicting node labels in weighted graphs, using random spanning trees to achieve near-optimal mistake bounds and demonstrating practical efficiency and accuracy on real datasets.

Contribution

The paper presents a novel randomized prediction method based on random spanning trees that achieves near-optimal mistake bounds for weighted graphs.

Findings

Algorithm achieves optimal mistake bounds up to logarithmic factors.

Method is faster and compares well with existing global and local algorithms.

Experiments confirm practical efficiency and accuracy on real-world data.

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.