Generalized Belief Propagation

By Jonathan S. Yedidia, William T. Freeman, Yair Weiss. 2000

1,230 citations recorded by the source corpus.

Subfields: Probabilistic & Bayesian Methods

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In Probabilistic & Bayesian Methods

Citations in the corpus

Discriminative Embeddings of Latent Variable Models for Structured Data (2016, positive): “The derivation of the fixed-point condition for loopy BP can be found in Yedidia et al. (2001b).”
Variational Inference: A Review for Statisticians (2016, methodology): “hasize that any procedure which uses optimization to approximate a density can be termed “variational inference.” This includes methods like expectation propagation (Minka, 2001), belief propagation (Yedidia et al., 2001), or even the Laplace approximation. We brieﬂy discuss alternative divergence m”
Kernel Belief Propagation (2011, methodology): “This will in turn lead to local marginal consistency conditions for learning with BP. Yedidia et al. (2001) showed that the fixed point of F (and therefore the global minimum {b?st, b?s}) must satisfy the relations b?st(Xs, Xt) = αΨst(Xs, Xt)Ψs(Xs)Ψt(Xt) ∏ u∈Γs\t m?us(Xs) ∏ v∈Γt\s m?vt(Xt),…”
Identification of direct residue contacts in protein–protein interaction by message passing (2009, background): “terms of belief propagation (17, 18) estimates only single-variable marginal”
Expectation Propagation for approximate Bayesian inference (2001, background): “For an undirected network with pairwise potentials, the EP energy function (13) is a dual representation of the Bethe free energy given by Yedidia et al. (2000).”
Optimal control as a graphical model inference problem (2009, neutral): “1999), the cluster variation method (CVM) or generalized belief propagation (GBP) (Yedidia et al. 2001) or Markov Chain Monte Carlo (MCMC) sampling methods.”
Efficient Solution Algorithms for Factored MDPs (2003, methodology): “We plan to leverage on ideas from loopy belief propagation algorithms for approximate inference in Bayesian networks (Pearl, 1988; Yedidia, Freeman, & Weiss, 2001 ) to address this issue.”
Recovering intrinsic images from a single image (2005, methodology): “We used the Generalized Belief Propagation algorithm [14] to infer the best label of each node in the MRF because ordinary Belief Propagation performed poorly in areas with both weak local evidence and strong compatibility constraints.”
Weight Uncertainty in Neural Network (2015, background): “The resulting cost function is variously known as the variational free energy (Neal and Hinton, 1998; Yedidia et al., 2000; Friston et al., 2007) or the expected lower bound (Saul et al.”
Image Mosaicing and Super-resolution (2004, background): “Mean-field or belief propagation [172] techniques may also offer an efficient method of solution.”
Constructing free-energy approximations and generalized belief propagation algorithms (2005, methodology): “Besides the results that we now discuss, which were first reported in [17], the interested reader can find similar empirical results for GBP algorithms in [58], [59], [56], [33], [49].”
ARACNE: An Algorithm for the Reconstruction of Gene Regulatory Networks in a Mammalian Cellular Context (2004, methodology): “It is, therefore, appealing that, for locally tree-like networks, the algorithm still works well, paralleling the corresponding discussion in statistical physics [38].”
Constraint satisfaction problems and neural networks: A statistical physics perspective. (2008, background): “To overcome the ﬁrst issue, generalized Belief Propagations (GBP) schemes have been proposed (Yedidia et al., 2001).”
Advanced Lectures on Machine Learning (2004, background): “Although the beliefs are not guaranteed to be correct on loopy graphs, interesting connections can be made to approximate inference procedures inspired by statistical physics known as the Bethe and Kikuchi free energies [45].”
Tree-reweighted belief propagation algorithms and approximate ML estimation by pseudo-moment matching (2003, methodology): “Observe that Algorithm 1, although quite similar to the standard belief propagation updates [11], diﬁers in some key ways.”