Submodular Relaxation for Inference in Markov Random Fields

IEEE Transactions on Pattern Analysis and Machine Intelligence. 2015. Vol. 37. No. 7. P. 1347–1359.

Осокин А. А., Ветров Д. П.

In this paper we address the problem of finding the most probable state of a discrete Markov random field (MRF), also known as the MRF energy minimization problem. The task is known to be NP-hard in general and its practical importance motivates numerous approximate algorithms. We propose a submodular relaxation approach (SMR) based on a Lagrangian relaxation of the initial problem. Unlike the dual decomposition approach of Komodakis et al., 2011 SMR does not decompose the graph structure of the initial problem but constructs a submodular energy that is minimized within the Lagrangian relaxation. Our approach is applicable to both pairwise and high-order MRFs and allows to take into account global potentials of certain types. We study theoretical properties of the proposed approach and evaluate it experimentally.

Ключевые слова: probabilistic graphical models