dc.contributor.author Wu, Baoyuan dc.contributor.author Shen, Li dc.contributor.author Zhang, Tong dc.contributor.author Ghanem, Bernard dc.date.accessioned 2020-03-08T06:55:02Z dc.date.available 2020-03-08T06:55:02Z dc.date.issued 2020-03-04 dc.date.submitted 2019-05-08 dc.identifier.citation Wu, B., Shen, L., Zhang, T., & Ghanem, B. (2020). MAP Inference Via ℓ2-Sphere Linear Program Reformulation. International Journal of Computer Vision. doi:10.1007/s11263-020-01313-2 dc.identifier.doi 10.1007/s11263-020-01313-2 dc.identifier.uri http://hdl.handle.net/10754/661924 dc.description.abstract Maximum a posteriori (MAP) inference is an important task for graphical models. Due to complex dependencies among variables in realistic models, finding an exact solution for MAP inference is often intractable. Thus, many approximation methods have been developed, among which the linear programming (LP) relaxation based methods show promising performance. However, one major drawback of LP relaxation is that it is possible to give fractional solutions. Instead of presenting a tighter relaxation, in this work we propose a continuous but equivalent reformulation of the original MAP inference problem, called LS–LP. We add the 2-sphere constraint onto the original LP relaxation, leading to an intersected space with the local marginal polytope that is equivalent to the space of all valid integer label configurations. Thus, LS–LP is equivalent to the original MAP inference problem. We propose a perturbed alternating direction method of multipliers (ADMM) algorithm to optimize the LS–LP problem, by adding a sufficiently small perturbation onto the objective function and constraints. We prove that the perturbed ADMM algorithm globally converges to the -Karush–Kuhn–Tucker (-KKT) point of the LS–LP problem. The convergence rate will also be analyzed. Experiments on several benchmark datasets from Probabilistic Inference Challenge (PIC 2011) and OpenGM 2 show competitive performance of our proposed method against state-of-the-art MAP inference methods. dc.publisher Springer Nature dc.relation.url http://link.springer.com/10.1007/s11263-020-01313-2 dc.rights Archived with thanks to International Journal of Computer Vision dc.title MAP Inference Via $\ell _2$-Sphere Linear Program Reformulation dc.type Article dc.contributor.department Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division dc.contributor.department Electrical Engineering Program dc.contributor.department VCC Analytics Research Group dc.identifier.journal International Journal of Computer Vision dc.rights.embargodate 2021-03-04 dc.eprint.version Post-print dc.contributor.institution Tencent AI Lab, Shenzhen 518000, China dc.contributor.institution Hong Kong University of Science and Technology, Hong Kong, China kaust.person Ghanem, Bernard dc.date.accepted 2020-02-20 dc.date.published-online 2020-03-04 dc.date.published-print 2020-07
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