Alpha-expansion is Exact on Stable Instances

Approximate algorithms for structured prediction problems—such as the popular αexpansion algorithm (Boykov et al. 2001) in computer vision—typically far exceed their theoretical performance guarantees on realworld instances. These algorithms often find solutions that are very close to optimal. The goal of this paper is to partially explain the performance of α-expansion on MAP inference in Ferromagnetic Potts models (FPMs). Our main results use the connection between energy minimization in FPMs and the Uniform Metric Labeling problem to give a stability condition under which the α-expansion algorithm provably recovers the optimal MAP solution. This theoretical result complements the numerous empirical observations of α-expansion’s performance. Additionally, we give a different stability condition under which an LP-based algorithm recovers the optimal solution.