NIPS Proceedingsβ

On the Convergence Rate of Decomposable Submodular Function Minimization

Part of: Advances in Neural Information Processing Systems 27 (NIPS 2014)

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Authors

Conference Event Type: Poster

Abstract

Submodular functions describe a variety of discrete problems in machine learning, signal processing, and computer vision. However, minimizing submodular functions poses a number of algorithmic challenges. Recent work introduced an easy-to-use, parallelizable algorithm for minimizing submodular functions that decompose as the sum of simple" submodular functions. Empirically, this algorithm performs extremely well, but no theoretical analysis was given. In this paper, we show that the algorithm converges linearly, and we provide upper and lower bounds on the rate of convergence. Our proof relies on the geometry of submodular polyhedra and draws on results from spectral graph theory."