The cost of learning directed cuts

Abstract

In this paper we investigate the problem of classifying vertices of a directed graph according to an unknown directed cut. We first consider the usual setting in which the directed cut is fixed. However, even in this setting learning is not possible without in the worst case needing the labels for the whole vertex set. By considering the size of the minimum path cover as a fixed parameter, we derive positive learnability results with tight performance guarantees for active, online, as well as PAC learning. The advantage of this parameter over possible alternatives is that it allows for an a priori estimation of the total cost of labelling all vertices. The main result of this paper is the analysis of learning directed cuts that depend on a hidden and changing context. © Springer-Verlag Berlin Heidelberg 2007.