Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Finding MAPs for belief networks is NP-hard
Artificial Intelligence
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
Tree consistency and bounds on the performance of the max-product algorithm and its generalizations
Statistics and Computing
Image Completion Using Global Optimization
CVPR '06 Proceedings of the 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition - Volume 1
Convergent Tree-Reweighted Message Passing for Energy Minimization
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Linear Programming Approach to Max-Sum Problem: A Review
IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Pattern Analysis and Machine Intelligence
Graphical Models, Exponential Families, and Variational Inference
Foundations and Trends® in Machine Learning
Message-passing for Graph-structured Linear Programs: Proximal Methods and Rounding Schemes
The Journal of Machine Learning Research
Convergent message passing algorithms: a unifying view
UAI '09 Proceedings of the Twenty-Fifth Conference on Uncertainty in Artificial Intelligence
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
MRF inference by k-fan decomposition and tight Lagrangian relaxation
ECCV'10 Proceedings of the 11th European conference on computer vision conference on Computer vision: Part III
MRF Energy Minimization and Beyond via Dual Decomposition
IEEE Transactions on Pattern Analysis and Machine Intelligence
Most probable explanations in Bayesian networks: Complexity and tractability
International Journal of Approximate Reasoning
Constructing free-energy approximations and generalized belief propagation algorithms
IEEE Transactions on Information Theory
MAP estimation via agreement on trees: message-passing and linear programming
IEEE Transactions on Information Theory
A bundle approach to efficient MAP-inference by Lagrangian relaxation
CVPR '12 Proceedings of the 2012 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)
Same-decision probability: A confidence measure for threshold-based decisions
International Journal of Approximate Reasoning
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We consider the problem of finding the most probable explanation (also known as the MAP assignment) on probabilistic graphical models. The dual decomposition algorithms based on coordinate descent are efficient approximate techniques for this problem, where the local dual functions are constructed and optimized to monotonically increase the cost of the dual function. In this paper, we present a unifying framework for constructing and optimizing these local dual functions, and introduce an energy distribution view to analyze the convergence rates of these algorithms. To optimize the local dual functions, we first propose a new concept-the energy distribution ratio-to describe the features of the solutions, and then derive an explicit optimal solution, which covers most of the monotonic dual decomposition algorithms. It is shown that the differences of these algorithms lie in both the forms of the local dual functions and the settings of the energy distribution ratios, and the existing algorithms mainly focus on constructing compact and solvable local dual functions. In contrast, we study the impact of the energy distribution ratios and introduce two energy distribution criteria for fast convergence. Moreover, we exploit dynamic energy distribution ratios to optimize the local dual functions, and propose a series of improved algorithms. The experimental results on synthetic and real problems show the improved algorithms outperform the existing ones on the convergence performance.