A strongly polynomial algorithm to solve combinatorial linear programs
Operations Research
Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
On the generation of alternative explanations with implications for belief revision
Proceedings of the seventh conference (1991) on Uncertainty in artificial intelligence
Finding MAPs for belief networks is NP-hard
Artificial Intelligence
A Pixel Dissimilarity Measure That Is Insensitive to Image Sampling
IEEE Transactions on Pattern Analysis and Machine Intelligence
Advanced inference in Bayesian networks
Learning in graphical models
Introduction to Linear Optimization
Introduction to Linear Optimization
A Taxonomy and Evaluation of Dense Two-Frame Stereo Correspondence Algorithms
International Journal of Computer Vision
Stereo Matching Using Belief Propagation
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part II
Solving Real-World Linear Programs: A Decade and More of Progress
Operations Research
Comparison of Graph Cuts with Belief Propagation for Stereo, using Identical MRF Parameters
ICCV '03 Proceedings of the Ninth IEEE International Conference on Computer Vision - Volume 2
What Energy Functions Can Be Minimizedvia Graph Cuts?
IEEE Transactions on Pattern Analysis and Machine Intelligence
ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1 - Volume 01
High-accuracy stereo depth maps using structured light
CVPR'03 Proceedings of the 2003 IEEE computer society conference on Computer vision and pattern recognition
Systematic vs. non-systematic algorithms for solving the MPE task
UAI'03 Proceedings of the Nineteenth conference on Uncertainty in Artificial Intelligence
Robust message-passing for statistical inference in sensor networks
Proceedings of the 6th international conference on Information processing in sensor networks
The Interplay of Optimization and Machine Learning Research
The Journal of Machine Learning Research
A Linear Programming Approach to Max-Sum Problem: A Review
IEEE Transactions on Pattern Analysis and Machine Intelligence
Graphical Models, Exponential Families, and Variational Inference
Foundations and Trends® in Machine Learning
International Journal of Computer Vision
Message-passing for Graph-structured Linear Programs: Proximal Methods and Rounding Schemes
The Journal of Machine Learning Research
Minimizing and learning energy functions for side-chain prediction
RECOMB'07 Proceedings of the 11th annual international conference on Research in computational molecular biology
On dual decomposition and linear programming relaxations for natural language processing
EMNLP '10 Proceedings of the 2010 Conference on Empirical Methods in Natural Language Processing
Norm-product belief propagation: primal-dual message-passing for approximate inference
IEEE Transactions on Information Theory
An alternating direction method for dual MAP LP relaxation
ECML PKDD'11 Proceedings of the 2011 European conference on Machine learning and knowledge discovery in databases - Volume Part II
Discriminative Models for Multi-Class Object Layout
International Journal of Computer Vision
Global Interactions in Random Field Models: A Potential Function Ensuring Connectedness
SIAM Journal on Imaging Sciences
Journal of Artificial Intelligence Research
Distributed Gibbs: a memory-bounded sampling-based DCOP algorithm
Proceedings of the 2013 international conference on Autonomous agents and multi-agent systems
DARWIN: a framework for machine learning and computer vision research and development
The Journal of Machine Learning Research
Joint inference of entities, relations, and coreference
Proceedings of the 2013 workshop on Automated knowledge base construction
Computer Vision and Image Understanding
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The problem of finding the most probable (MAP) configuration in graphical models comes up in a wide range of applications. In a general graphical model this problem is NP hard, but various approximate algorithms have been developed. Linear programming (LP) relaxations are a standard method in computer science for approximating combinatorial problems and have been used for finding the most probable assignment in small graphical models. However, applying this powerful method to real-world problems is extremely challenging due to the large numbers of variables and constraints in the linear program. Tree-Reweighted Belief Propagation is a promising recent algorithm for solving LP relaxations, but little is known about its running time on large problems. In this paper we compare tree-reweighted belief propagation (TRBP) and powerful general-purpose LP solvers (CPLEX) on relaxations of real-world graphical models from the fields of computer vision and computational biology. We find that TRBP almost always finds the solution significantly faster than all the solvers in CPLEX and more importantly, TRBP can be applied to large scale problems for which the solvers in CPLEX cannot be applied. Using TRBP we can find the MAP configurations in a matter of minutes for a large range of real world problems.