Prediction on a Graph with the Perceptron
Mark Herbster and Massimiliano Pontil
In: NIPS 2006, December 2006, Vancouver, CA.
We study the problem of online prediction of a noisy labeling of a graph
with the perceptron. We address both label noise and concept noise.
Graph learning is framed as an instance of prediction on a finite set.
To treat label noise we show that the hinge loss bounds derived by
Gentile for online perceptron learning can be transformed to relative mistake bounds with an optimal leading constant when applied
to prediction on a finite set. These bounds depend
crucially on the norm of the learned concept. Often the norm of a concept can
vary dramatically with only small perturbations in a labeling.
We analyze a simple transformation that stabilizes the norm
under perturbations. We derive an upper bound that depends only on natural properties of the graph --
the graph diameter and the cut size of a partitioning of the graph -- which are
only indirectly dependent on the size of the graph. The impossibility of such
bounds for the graph geodesic nearest neighbors algorithm will be demonstrated.