Introduction to Linear Optimization
Introduction to Linear Optimization
Convex Optimization
Solving Markov Random Fields using Second Order Cone Programming Relaxations
CVPR '06 Proceedings of the 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition - Volume 1
Proceedings of the 25th international conference on Machine learning
On the optimality of solutions of the max-product belief-propagation algorithm in arbitrary graphs
IEEE Transactions on Information Theory
Tree-based reparameterization framework for analysis of sum-product and related algorithms
IEEE Transactions on Information Theory
MAP estimation via agreement on trees: message-passing and linear programming
IEEE Transactions on Information Theory
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A class of Maximum A Posteriori(MAP) formulations built on various graph models are of great interests for both theoretical and practical applications. Recent advances in this field have extended the connections between the linear program (LP) relaxation and various tree-reweighted message passing algorithms. At both sides, many algorithms and their optimality certificates are proved, provided no conflict exists between the node marginal maximum and the corresponding edge marginal maximum. However, these conflicts are usually inevitable for general non-trivial Markov random fields (MRFs). Our work is aimed at reducing such conflicts by reparameterizing the original energy distributions in pairwise Markov random field. All node potentials will be decomposed and attached to local edges according to their local graph structures. And thus, only edge marginals are needed in our linear program relaxation, and the node marginals are only used to exchange information among different parts of the graph. We incorporated this consistent graph-structured reparameterization into some latest LP optimality guaranteed proximal solvers, and the resulted algorithms outperform the original ones in convergence rate and also have a better behavior to converge to MAP optimality monotonously even for some highly noisy MRFs.