Bethe free energy, Kikuchi approximations, and belief propagation algorithms

By Jonathan S. Yedidia, William T. Freeman, Yair Weiss. 2001

244 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).”
Empirical Risk Minimization of Graphical Model Parameters Given Approximate Inference, Decoding, and Model Structure (2011, background): “The resulting beliefs can be combined into a quantity called the Bethe free energy that approximates − logZ (Yedidia et al., 2000).”
Inverse statistical problems: from the inverse Ising problem to data science (2017, background): “Then equations (96) and (97) then read = artanh( m i ), the ﬁrst order contribution of the free energy (102) leads to”
Constructing free-energy approximations and generalized belief propagation algorithms (2005, result): “We have also previously released a number of technical reports [33], [ 34 ], [35] that are largely superseded by this paper, as well as a somewhat more popular introduction [36].”
Codes on graphs: normal realizations (2000, background): “The pairwise restriction allows a number of remarkable results to be proved [50].”
Wild Variational Approximations (2016, methodology): “We present all these proposals in VI context (which is then named wild variational inference), although they can be extended to other methods such as Bethe free energy [14, 15] and α-divergence methods [16, 17].”
New Outer Bounds on the Marginal Polytope (2007, background): “Belief propagation can be seen as optimizing pseudomarginals over LOCAL(G) with a (non-convex) Bethe approximation to the entropy [15].”
A Bayesian network framework for relational shape matching (2003, background): “By leveraging recent developments in Bayesian networks— notably the Bethe free energy approach [30]—we show that efficient relational shape matching algorithms can be designed.”
Combining Phylogenetic and Hidden Markov Models in Biosequence Analysis (2003, methodology): “As future work, we hope to compare this “empirical” model with process-based models, using MCMC or one of the approximation techniques available for graphical models with “loops” of dependency (Murphy et al., 1999; Wainwright et al., 2001; Yedidia et al., 2001).”