Submodular Relaxation for Inference in Markov Random Fields

Anton Osokin (1, 2) , Dmitry P. Vetrov (3, 4)

1 SIERRA - Statistical Machine Learning and Parsimony
2 LIENS - Laboratoire d'informatique de l'école normale supérieure
3 Skoltech - Skolkovo Institute of Science and Technology [Moscow]
4 HSE - Vysšaja škola èkonomiki = National Research University Higher School of Economics [Moscow]

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. [29] 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.

Mots clés: Markov random fields; energy minimization; graph cuts; combinatorial algorithms; relaxation

Domaines: Algorithme et structure de données [cs.DS]; Machine Learning [stat.ML]

Anton Osokin, Dmitry P. Vetrov. Submodular Relaxation for Inference in Markov Random Fields. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2015, 37 (7), pp.14. ⟨10.1109/TPAMI.2014.2369046⟩. ⟨hal-01103488⟩