Reflection methods for user-friendly submodular optimization

Stefanie Jegelka (1) , Francis Bach (2, 3) , Suvrit Sra (4)

1 LBNL - Lawrence Berkeley National Laboratory [Berkeley]
2 SIERRA - Statistical Machine Learning and Parsimony
3 LIENS - Laboratoire d'informatique de l'école normale supérieure
4 Max Planck Institute for Intelligent Systems [Tübingen]

Recently, it has become evident that submodularity naturally captures widely occurring concepts in machine learning, signal processing and computer vision. Consequently, there is need for efficient optimization procedures for submodular functions, especially for minimization problems. While general submodular minimization is challenging, we propose a new method that exploits existing decomposability of submodular functions. In contrast to previous approaches, our method is neither approximate, nor impractical, nor does it need any cumbersome parameter tuning. Moreover, it is easy to implement and parallelize. A key component of our method is a formulation of the discrete submodular minimization problem as a continuous best approximation problem that is solved through a sequence of reflections, and its solution can be easily thresholded to obtain an optimal discrete solution. This method solves both the continuous and discrete formulations of the problem, and therefore has applications in learning, inference, and reconstruction. In our experiments, we illustrate the benefits of our method on two image segmentation tasks.

Domaines: Apprentissage [cs.LG]; Optimisation et contrôle [math.OC]; Recherche opérationnelle [math.OC]

Stefanie Jegelka, Francis Bach, Suvrit Sra. Reflection methods for user-friendly submodular optimization. NIPS 2013 - Neural Information Processing Systems, Dec 2013, Lake Tahoe, Nevada, United States. ⟨hal-00905258⟩