Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
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
Journal of Functional Programming
Graph Theory
Graphical Models, Exponential Families, and Variational Inference
Foundations and Trends® in Machine Learning
Convexifying the Bethe free energy
UAI '09 Proceedings of the Twenty-Fifth Conference on Uncertainty in Artificial Intelligence
Probabilistic Graphical Models: Principles and Techniques - Adaptive Computation and Machine Learning
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
Constructing free-energy approximations and generalized belief propagation algorithms
IEEE Transactions on Information Theory
A new class of upper bounds on the log partition function
IEEE Transactions on Information Theory
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Inference on cyclic graphs is one of the most important problems in the applications of graphical models. While exact inference is NP-hard on general cyclic graphs, it has been found that exact inference can be achieved with a computational complexity as low as O(Nm^3) on the outer-planar graph, which is a special kind of cyclic graph. In this paper, we introduce a new kind of cyclic graph, the generalized outer-planar (GOP) graph, which is more general than the outer-planar graph and show that the exact inference on the GOP graphs can be achieved in O(Nm^3) by a recursive sum-product (RSP) algorithm. RSP exploits the property of GOP graphs that the faces are reducible, and brings a ''face elimination'' procedure to compute the marginals exactly. Furthermore, RSP can be implemented on general cyclic graphs to obtain approximate marginals. Experimental results show the effectiveness of approximate RSP on various graphical models.