@Article{Werner-Kiev-2011, IS = { zkontrolovano 10 Jan 2012 }, UPDATE = { 2011-12-29 }, author = {Werner, Tom{\'a}{\v s}}, title = {How to Compute Primal Solution from Dual One in LP Relaxation of MAP Inference in MRF? }, year = {2011}, month = {March--April}, pages = {86--93}, journal = {Control Systems and Computers}, publisher = {National Academy of Sciences of Ukraine}, address = {Kiev, Ukraine}, issn = {0130-5395}, volume = {2011}, number = {2}, authorship = {100}, annote = {In LP relaxation of MAP inference in Markov random fields (MRF), the primal LP maximizes the MAP objective over relaxed labelings (pseudomarginals) and the dual LP minimizes an upper bound on the true MAP solution by reparameterizations. Having solved the dual~LP, we have no direct access to the corresponding primal solution. We propose a simple way to compute an optimal primal solution from an optimal dual solution. Precisely, we given an algorithm that either shows that the upper bound for a given problem can be further decreased by reparameterizations (i.e., it is not dual-optimal) or computes the corresponding optimal relaxed labeling. This is done by first removing inactive dual constraints and then solving the resulting feasibility problem by a very simple message-passing algorithm, sum-product diffusion.}, keywords = {weighted constraint satisfaction, arc consistency, Markov random fields }, project = {FP7-ICT-247022 MASH only EU, MSM6840770038}, psurl = { [PDF]}, }