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Linearized and Single-Pass Belief Propagation [article]

Wolfgang Gatterbauer, Stephan Günnemann, Danai Koutra, Christos Faloutsos
2014 arXiv   pre-print
The paper also introduces Single-pass Belief Propagation (SBP), a "localized" version of LinBP that propagates information across every edge at most once and for which the final class assignments depend  ...  This paper introduces Linearized Belief Propagation (LinBP), a linearization of BP that allows a closed-form solution via intuitive matrix equations and, thus, comes with convergence guarantees.  ...  We would like to thank Garry Miller for pointing us to Roth's column lemma and the anonymous reviewers for their careful reading and detailed feedback.  ... 
arXiv:1406.7288v4 fatcat:chnmq272nbacbcwx7lo5zdz5k4

Linearized and single-pass belief propagation

Wolfgang Gatterbauer, Stephan Günnemann, Danai Koutra, Christos Faloutsos
2015 Proceedings of the VLDB Endowment  
The paper also introduces Single-pass Belief Propagation (SBP), a localized (or "myopic") version of LinBP that propagates information across every edge at most once and for which the final class assignments  ...  This paper introduces Linearized Belief Propagation (LinBP), a linearization of BP that allows a closed-form solution via intuitive matrix equations and, thus, comes with exact convergence guarantees.  ...  This work was supported in part by NSF grants IIS-1217559 and IIS-1408924.  ... 
doi:10.14778/2735479.2735490 fatcat:5qpuiqszezdypbqc3pli6hyeey

Expectation Propogation for approximate inference in dynamic Bayesian networks [article]

Tom Heskes, Onno Zoeter
2012 arXiv   pre-print
We describe expectation propagation for approximate inference in dynamic Bayesian networks as a natural extension of Pearl s exact belief propagation.Expectation propagation IS a greedy algorithm, converges  ...  correspond TO local minima OF this free energy, but that the converse need NOT be the CASE .We illustrate the algorithms BY applying them TO switching linear dynamical systems AND discuss implications  ...  Acknowledgements We would like to thank Tay lan Cemgil for helpful in put and acknowledge support by the Dutch Technol ogy Foundation STW and the Dutch Centre of Com petence Paper and Board.  ... 
arXiv:1301.0572v1 fatcat:rzeyzwcj5ff4bf35a5csdylhea

A differential semantics for jointree algorithms

James D. Park, Adnan Darwiche
2004 Artificial Intelligence  
According to this approach, belief network inference reduces to a simple process of evaluating and differentiating multi-linear functions.  ...  A new approach to inference in belief networks has been recently proposed, which is based on an algebraic representation of belief networks using multi-linear functions.  ...  Acknowledgement This work has been partially supported by NSF grant IIS-9988543 and MURI grant N00014-00-1-0617.  ... 
doi:10.1016/j.artint.2003.04.004 fatcat:sjozzzsd6jbt7aepkanozipu4m

A differential semantics for jointree algorithms

J PARK
2004 Artificial Intelligence  
According to this approach, belief network inference reduces to a simple process of evaluating and differentiating multi-linear functions.  ...  A new approach to inference in belief networks has been recently proposed, which is based on an algebraic representation of belief networks using multi-linear functions.  ...  Acknowledgement This work has been partially supported by NSF grant IIS-9988543 and MURI grant N00014-00-1-0617.  ... 
doi:10.1016/s0004-3702(04)00029-3 fatcat:plsw6cfxgrenxc4cploe7uq2ey

Tracking and smoothing of time-varying sparse signals via approximate belief propagation

Justin Ziniel, Lee C. Potter, Philip Schniter
2010 2010 Conference Record of the Forty Fourth Asilomar Conference on Signals, Systems and Computers  
Built on the belief propagation framework, the algorithm leverages recently developed approximate message passing techniques to perform rapid and accurate estimation.  ...  The algorithm is capable of performing both causal tracking and non-causal smoothing to enable both online and offline processing of sparse time series, with a complexity that is linear in all problem  ...  At this point we have completed what we term a single forward/backward pass.  ... 
doi:10.1109/acssc.2010.5757677 fatcat:eawfcnstlveynh2e3gfkwp66di

On the geometry of message passing algorithms for Gaussian reciprocal processes

Francesca Paola Carli
2016 2016 IEEE 55th Conference on Decision and Control (CDC)  
Second, we establish a link between convergence analysis of belief propagation for Gaussian reciprocal processes and stability theory for differentially positive systems.  ...  First, we introduce belief propagation for Gaussian reciprocal processes.  ...  Gaussian Belief Propagation for a Hidden Reciprocal ModelFor Gaussian distributed variables, messages and beliefs are Gaussians and the belief propagation updates can be written explicitly in terms of  ... 
doi:10.1109/cdc.2016.7798965 dblp:conf/cdc/Carli16 fatcat:itttyiu6prgwvie5o2idkfcx4q

A visual introduction to Gaussian Belief Propagation [article]

Joseph Ortiz, Talfan Evans, Andrew J. Davison
2021 arXiv   pre-print
A special case of loopy belief propagation, GBP updates rely only on local information and will converge independently of the message schedule.  ...  In this article, we present a visual introduction to Gaussian Belief Propagation (GBP), an approximate probabilistic inference algorithm that operates by passing messages between the nodes of arbitrarily  ...  We would particularly like to thank Xiaofan Mu, Raluca Scona, Riku Murai, Edgar Sucar, Seth Nabarro, Tristan Laidlow, Nanfeng Liu, Shuaifeng Zhi, Kentara Wada and Stefan Leutenegger.  ... 
arXiv:2107.02308v1 fatcat:kg273hpwnbfiraeznofb2jhqeq

Fixing convergence of Gaussian belief propagation

Jason K. Johnson, Danny Bickson, Danny Dolev
2009 2009 IEEE International Symposium on Information Theory  
Gaussian belief propagation (GaBP) is an iterative message-passing algorithm for inference in Gaussian graphical models.  ...  We believe that our construction has numerous applications, since the GaBP algorithm is linked to solution of linear systems of equations, which is a fundamental problem in computer science and engineering  ...  INTRODUCTION The Gaussian belief propagation algorithm (GaBP) is an efficient distributed message-passing algorithm for computing inference over a Gaussian graphical model.  ... 
doi:10.1109/isit.2009.5205777 dblp:conf/isit/DolevBJ09 fatcat:obhq7uia4jer5nwre2wwur45ku

A note on MCMC for nested multilevel regression models via belief propagation [article]

Omiros Papaspiliopoulos, Giacomo Zanella
2017 arXiv   pre-print
We show that nested multilevel regression models with Gaussian errors lend themselves very naturally to the combined use of belief propagation and MCMC.  ...  propagation at a cost that scales linearly in the number of parameters and data.  ...  The forward pass of belief propagation computes messages going from the leaves to the root and the backward pass computes messages from the root to the leaves.  ... 
arXiv:1704.06064v2 fatcat:ywaogkuy7rfarmd7dzozb63bou

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

Brian Potetz, Tai Sing Lee
2008 Computer Vision and Image Understanding  
belief propagation.  ...  In this paper, we introduce a new technique to compute belief propagation messages in time linear with respect to clique size for a large class of potential functions over real-valued variables.  ...  Potetz and NSF IIS-0413211 and NSF IIS-0713206 to T.S. Lee.  ... 
doi:10.1016/j.cviu.2008.05.007 fatcat:okprf3zcqngnrhws6emglpcs6m

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

Thomas Parr, Dimitrije Markovic, Stefan J. Kiebel, Karl J. Friston
2019 Scientific Reports  
While variational message passing offers a simple and neuronally plausible architecture, it falls short of the inferential performance of belief propagation.  ...  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

Single-channel speech separation and recognition using loopy belief propagation

Steven J. Rennie, John R. Hershey, Peder A. Olsen
2009 2009 IEEE International Conference on Acoustics, Speech and Signal Processing  
We address the problem of single-channel speech separation and recognition using loopy belief propagation in a way that enables efficient inference for an arbitrary number of speech sources.  ...  The combination of sources is modeled in the log spectrum domain using non-linear interaction functions.  ...  In this paper, we present a loopy belief propagation algorithm for multi-talker speech separation and recognition using a single channel.  ... 
doi:10.1109/icassp.2009.4960466 dblp:conf/icassp/RennieHO09 fatcat:j3zy4yvxzrervgqqqzyv4h3qf4

Bayesian Classifiers for Chemical Toxicity Prediction

Meenakshi Mishra, Brian Potetz, Jun Huan
2011 2011 IEEE International Conference on Bioinformatics and Biomedicine  
The challenge here is that the growth in the number of chemicals is fast, and the traditional standards for toxicity testing involve a slow and expensive process of in vivo animal testing.  ...  IEEE International Conference on Bioinformatics and Biomedicine 978-0-7695-4574-5/11 $26.00  ...  An alternative message-passing algorithm for computing the mean of P(h|Z) is Belief Propagation (BP).  ... 
doi:10.1109/bibm.2011.109 dblp:conf/bibm/MishraPH11 fatcat:5f3s6f37erfqhe54n3f7cwwrwa

Pseudo Prior Belief Propagation for densely connected discrete graphs

Jacob Goldberger, Amir Leshem
2010 IEEE Information Theory Workshop 2010 (ITW 2010)  
Hence, applying the Belief Propagation (BP) algorithm yields very poor results.  ...  Next we integrate this information into a loopy Belief Propagation (BP) algorithm as a pseudo prior.  ...  THE LOOPY BELIEF PROPAGATION APPROACH Given the constrained linear system y = Hx + ǫ, and a uniform prior distribution on x, the posterior probability function of the discrete random vector x given y is  ... 
doi:10.1109/itwksps.2010.5503198 fatcat:krgiu3uxyfa4biowrf7sy36bfy
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