Revisiting Decomposable Submodular Function Minimization with Incidence Relations

Part of Advances in Neural Information Processing Systems 31 (NeurIPS 2018)

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Pan Li, Olgica Milenkovic


We introduce a new approach to decomposable submodular function minimization (DSFM) that exploits incidence relations. Incidence relations describe which variables effectively influence the component functions, and when properly utilized, they allow for improving the convergence rates of DSFM solvers. Our main results include the precise parametrization of the DSFM problem based on incidence relations, the development of new scalable alternative projections and parallel coordinate descent methods and an accompanying rigorous analysis of their convergence rates.