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Efficient Belief Propagation with Learned Higher-Order Markov Random Fields [chapter]

Xiangyang Lan, Stefan Roth, Daniel Huttenlocher, Michael J. Black
2006 Lecture Notes in Computer Science  
In particular, we show how both pairwise and higher-order Markov random fields with learned clique potentials capture rich image structures that better represent the properties of natural images.  ...  Belief propagation (BP) has become widely used for low-level vision problems and various inference techniques have been proposed for loopy graphs.  ...  In the following sections we introduce Markov random fields and loopy belief propagation along with our proposed approximations.  ... 
doi:10.1007/11744047_21 fatcat:r3be7rj6jbey3ibjec2hkydali

Efficient Belief Propagation for Vision Using Linear Constraint Nodes

Brian Potetz
2007 2007 IEEE Conference on Computer Vision and Pattern Recognition  
Belief propagation over pairwise connected Markov Random Fields has become a widely used approach, and has been successfully applied to several important computer vision problems.  ...  Unfortunately, the complexity of belief propagation is exponential in the size of the largest clique.  ...  Roth & the authors of [10] for graciously sharing filters & results. This research was funded by an NSF Graduate Research Fellowship to the author and NSF IIS-0413211 to TS Lee.  ... 
doi:10.1109/cvpr.2007.383094 dblp:conf/cvpr/Potetz07 fatcat:xlnxdwp46rew5gcsd5ibklgbsa

Diffusion Methods for Classification with Pairwise Relationships [article]

Pedro F. Felzenszwalb, Benar F. Svaiter
2019 arXiv   pre-print
We prove that the fixed points of the algorithms under consideration define lower-bounds on the energy function and the max-marginals of a Markov random field.  ...  The approach is also related to message passing algorithms, including belief propagation and mean field methods.  ...  Energy minimization methods based on Markov random fields (MRF) address these problems in a common framework [3, 21, 14] .  ... 
arXiv:1505.06072v4 fatcat:2xetclczkrhuvdy35nlynbi36a

Diffusion methods for classification with pairwise relationships

Pedro F. Felzenszwalb, Benar F. Svaiter
2019 Quarterly of Applied Mathematics  
We prove that the fixed points of the algorithms under consideration define lower-bounds on the energy function and the max-marginals of a Markov random field.  ...  The algorithms involve contraction maps and are related to non-linear diffusion and random walks on graphs. The approach is also related to message passing and mean field methods.  ...  Energy minimization methods based on Markov random fields (MRF) address these problems in a common framework [3, 18, 14] .  ... 
doi:10.1090/qam/1540 fatcat:5qeeb6wxprchdegosc6wgemzci

Efficient belief propagation for higher-order cliques using linear constraint nodes

Brian Potetz, Tai Sing Lee
2008 Computer Vision and Image Understanding  
Belief propagation over pairwise-connected Markov random fields has become a widely used approach, and has been successfully applied to several important computer vision problems.  ...  Unfortunately, the complexity of belief propagation is exponential in the size of the largest clique.  ...  Roth and the authors of [5] for graciously sharing filters & results.  ... 
doi:10.1016/j.cviu.2008.05.007 fatcat:okprf3zcqngnrhws6emglpcs6m

Consensus Estimation via Belief Propagation

Huaiyu Dai, Yanbing Zhang
2007 2007 41st Annual Conference on Information Sciences and Systems  
The discussion is also extended to the application of estimating a Markov random field. I.  ...  The belief propagation algorithm is adopted to provide a common information processing and dissemination framework for such a purpose.  ...  In this subsection, we consider the application of field gathering where X is a Gaussian Markov random field and each node only observes a spatial component i X of it.  ... 
doi:10.1109/ciss.2007.4298313 dblp:conf/ciss/DaiZ07 fatcat:3jkwmq7ugfcupkczmrjthllo4q

Random Fields in Physics, Biology and Data Science

Enrique Hernández-Lemus
2021 Frontiers in Physics  
A random field is the representation of the joint probability distribution for a set of random variables.  ...  For strictly positive probability densities, a Markov random field is also a Gibbs field, i.e., a random field supplemented with a measure that implies the existence of a regular conditional distribution  ...  Based on the neighborhood structure of a pairwise Markov random field, posterior probabilities are computed via a loopy belief propagation algorithm.  ... 
doi:10.3389/fphy.2021.641859 fatcat:2bi74vqkureefmtzwinma2yiwq

Enforcing Consistency In Spectral Masks Using Markov Random Fields

Michael Mandel, Nicoleta Roman
2015 Zenodo  
Publication in the conference proceedings of EUSIPCO, Nice, France, 2015  ...  Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.  ...  Acknowledgements This material is based upon work supported by the National Science Foundation under Grant No. IIS-1409431.  ... 
doi:10.5281/zenodo.38889 fatcat:2erqsfva2raifh524iwnqpjjpe

Structured variational methods for distributed inference in wireless ad hoc and sensor networks

Yanbing Zhang, Huaiyu Dai
2009 2009 IEEE International Conference on Acoustics, Speech and Signal Processing  
In this paper, a variational message passing framework is proposed for Markov random fields, which is computationally more efficient and admits wider applicability compared to the belief propagation algorithm  ...  Its performance is elaborated on a Gaussian Markov random field, through both theoretical analysis and simulation results .  ...  Assume is a Gaussian pairwise Markov random field and each node is only associated to a spatial component X i X of it.  ... 
doi:10.1109/icassp.2009.4960198 dblp:conf/icassp/ZhangD09 fatcat:tq6kbfvj7bduzjp6atf7hwm4la

Distributed Convergence Verification for Gaussian Belief Propagation [article]

Jian Du, Soummya Kar, José M. F. Moura
2017 arXiv   pre-print
In this paper, we propose a novel sufficient convergence condition for Gaussian BP that applies to both the pairwise linear Gaussian model and to Gaussian Markov random fields.  ...  Gaussian belief propagation (BP) is a computationally efficient method to approximate the marginal distribution and has been widely used for inference with high dimensional data as well as distributed  ...  Gaussian Markov Random Field In the domain of physics and probability, a Markov random field (often abbreviated as MRF), Markov network, or undirected graphical model is a set of random variables having  ... 
arXiv:1711.09888v1 fatcat:uzjfomjo4vh5negxywlgtm3jtm

A recommender system based on Belief Propagation over Pairwise Markov Random Fields

Erman Ayday, Jun Zou, Arash Einolghozati, Faramarz Fekri
2012 2012 50th Annual Allerton Conference on Communication, Control, and Computing (Allerton)  
In this paper, we formulate the recommendation problem as an inference problem on a Pairwise Markov Random Field (PMRF), where nodes representing items are connected with each other to exploit item-based  ...  Thus, we utilize the Belief Propagation (BP) algorithm to solve the problem with a complexity that grows linearly with the number of items in the system.  ...  CONCLUSION In this paper, we solve the recommender system problem using Belief Propagation (BP) algorithm on a Pairwise Markov Random Field (PMRF).  ... 
doi:10.1109/allerton.2012.6483287 dblp:conf/allerton/AydayZEF12 fatcat:fe67msl7eva4hkpxppinjhhdzm

Approximate covariance estimation in graphical approaches to SLAM

Gian Diego Tipaldi, Giorgio Grisetti, Wolfram Burgard
2007 2007 IEEE/RSJ International Conference on Intelligent Robots and Systems  
In experiments we demonstrate that our approach outperforms two commonly used techniques, namely loopy belief propagation and belief propagation on a spanning tree.  ...  Most of the existing techniques focus mainly on determining the most likely map and leave open how to efficiently compute the marginal covariances.  ...  ACKNOWLEDGMENT This work has partly been supported by the EC under contract number FP6-IST-34120, Action Line: 2.5.2.: Micro/Nano Based Subsystems.  ... 
doi:10.1109/iros.2007.4399258 dblp:conf/iros/TipaldiGB07 fatcat:mfcko2bptber7aoxzgeydwizmu

Neuronal message passing using Mean-field, Bethe, and Marginal approximations

Thomas Parr, Dimitrije Markovic, Stefan J. Kiebel, Karl J. Friston
2019 Scientific Reports  
In contrast, belief propagation allows exact computation of marginal posteriors at the expense of the architectural simplicity of variational message passing.  ...  These are variational message passing and belief propagation - each of which is derived from a free energy functional that relies upon different approximations (mean-field and Bethe respectively).  ...  This work was supported by the Deutsche Forschungsgemeinschaft (SFB 940/2, Project A9) and by the TU Dresden Graduate Academy.  ... 
doi:10.1038/s41598-018-38246-3 pmid:30760782 pmcid:PMC6374414 fatcat:3u6w7kywufdw7hgqck5lalmhf4

Convergence analysis of belief propagation for pairwise linear Gaussian models [article]

Jian Du, Shaodan Ma, Yik-Chung Wu, Soummya Kar, José M. F. Moura
2017 arXiv   pre-print
In this paper, we analyze the convergence properties of Gaussian BP for this pairwise linear Gaussian model.  ...  Gaussian belief propagation (BP) has been widely used for distributed inference in large-scale networks such as the smart grid, sensor networks, and social networks, where local measurements/observations  ...  (also known as Markov random field (MRF)).  ... 
arXiv:1706.04074v4 fatcat:va37epryxbdlhdc34tqegdwdhu

Linear Response Algorithms for Approximate Inference in Graphical Models

Max Welling, Yee Whye Teh
2004 Neural Computation  
Applying these ideas to Gaussian random fields we derive a propagation algorithm for computing the inverse of a matrix.  ...  In this paper we propose two new algorithms for approximating these pairwise probabilities, based on the linear response theorem.  ...  Acknowledgements We would like to thank Martin Wainwright for discussion and the referees for valuable feedback. MW would like to thank Geoffrey Hinton for support.  ... 
doi:10.1162/08997660460734056 pmid:15006029 fatcat:2lbwsi7w7ranfkzdd6xizaypbu
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