Alpha-expansion is Exact on Stable Instances
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Approximate algorithms for structured prediction problems---such as the popular alpha-expansion algorithm (Boykov et al. 2001) in computer vision---typically far exceed their theoretical performance guarantees on real-world instances. These algorithms often find solutions that are very close to optimal. The goal of this paper is to partially explain the performance of alpha-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 alpha-expansion algorithm provably recovers the optimal MAP solution. This theoretical result complements the numerous empirical observations of alpha-expansion's performance. Additionally, we give a different stability condition under which an LP-based algorithm recovers the optimal solution.
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