Tree-reweighted belief propagation algorithms and approximate ML estimation by pseudo-moment matching

By Martin J. Wainwright, Tommi S. Jaakkola, Alan S. Willsky. 2003

250 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, background): “…BP and damped BP. C.3 Tree-reweighted BP Different from loopy BP and its variants which optimizing the Bethe free energy, the tree-reweighted BP (Wainwright et al., 2003) is optimizing a convexified Bethe energy, min {qij}(i,j∈E) L = ∑ i ∫ H q(hi) log q(hi)dhi + ∑ i,j vij ∫ H2 qij(hi, hj) log…”
Kernel Belief Propagation (2011, methodology): “Therefore once again, edge potentials were selected using the technique described in Wainwright et al. (2003).”
Taming the Curse of Dimensionality: Discrete Integration by Hashing and Optimization (2013, methodology): “For comparison, we consider Tree Reweighted Belief Propagation [31] which provides an upper bound on Z, Mean Field [32] which provides a lower bound, and Loopy Belief Propagation [20] which provides an estimate with no guarantees.”
Deep Learning and Structured Prediction for the Segmentation of Mass in Mammograms (2015, methodology): “Tree re-weighted (TRW) belief propagation provides an upper bound to this log-partition function [6]:”
Inductive Principles for Restricted Boltzmann Machine Learning (2010, methodology): “Examples of the approximation approach include stochastic approximation-based maximum likelihood learning methods (Younes, 1989), as well as approximation methods based on belief propagation (Wainwright et al., 2003).”
Graphical Models, Exponential Families, and Variational Inference (2008, methodology): “We summarize our findings in the following result [238, 241]:”
Convergence Rates of Inexact Proximal-Gradient Methods for Convex Optimization (2011, methodology): “For example, errors in the calculation of the gradient arise when fitting undirected graphical models and using an iterative method to approximate the gradient of the log-partition function [37].”
Blending Learning and Inference in Conditional Random Fields (2016, background): “The reminder of the paper is organized as follows.”
A Linear Programming Approach to Max-Sum Problem: A Review (2007, methodology): “TRW and tree combination were considered in a broader view including other inference problems on graphical models [WJW03b,WJ03a,WJ03b].”
Greedy Direction Method of Multiplier for MAP Inference of Large Output Domain (2017, methodology): “This non-smoothness also hinders global convergence for algorithms that replace the Subgradient Descent with the Block Coordinate Descent, such as TreeReweighted Belief Propagation (TRWBP) [15], TreeReweighted max-product message passing with Sequential update(TRW-S) [7], and Max-Product Linear Prog”
Learning in Markov Random Fields using Tempered Transitions (2009, methodology): “When using variational methods, such as loopy BP [18] and TRBP [16], learning often gets trapped in poor local optima [5, 13].”
Estimating the "Wrong" Graphical Model: Benefits in the Computation-Limited Setting (2006, methodology): “For the tree-reweighted Bethe surrogate (13), we have shown in previous work (Wainwright et al., 2003b) that in the absence of regularization, the optimal parameter estimates θ n have a very simple closed-form solution, specified in terms of the weights ρ st and the empirical marginals µ. (We make…”
A new class of upper bounds on the log partition function (2002, methodology): “This surrogate has a number of possible applications to parameter estimation, as our initial work [38] in this direction has suggested.”
Learning to Combine Bottom-Up and Top-Down Segmentation (2006, methodology): “In this work we have approximated the marginal probabilities and the partition function using sum product tree-reweighted belief propagation (Wainwright et al. 2003), which provides a rigorous bound on the partition function, and has better convergence properties than standard belief propagation.”