Stochastic reasoning, free energy, and information geometry
Neural Computation
Convergent Tree-Reweighted Message Passing for Energy Minimization
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Linear Programming Approach to Max-Sum Problem: A Review
IEEE Transactions on Pattern Analysis and Machine Intelligence
Convexity arguments for efficient minimization of the Bethe and Kikuchi free energies
Journal of Artificial Intelligence Research
Loopy belief propagation for approximate inference: an empirical study
UAI'99 Proceedings of the Fifteenth conference on Uncertainty in artificial intelligence
Constructing free-energy approximations and generalized belief propagation algorithms
IEEE Transactions on Information Theory
A new class of upper bounds on the log partition function
IEEE Transactions on Information Theory
MAP estimation via agreement on trees: message-passing and linear programming
IEEE Transactions on Information Theory
Norm-product belief propagation: primal-dual message-passing for approximate inference
IEEE Transactions on Information Theory
Joint training for open-domain extraction on the web: exploiting overlap when supervision is limited
Proceedings of the fourth ACM international conference on Web search and data mining
Collective Inference for Extraction MRFs Coupled with Symmetric Clique Potentials
The Journal of Machine Learning Research
MICCAI'11 Proceedings of the 14th international conference on Medical image computing and computer-assisted intervention - Volume Part III
Global Interactions in Random Field Models: A Potential Function Ensuring Connectedness
SIAM Journal on Imaging Sciences
Structured Learning and Prediction in Computer Vision
Foundations and Trends® in Computer Graphics and Vision
Energy distribution view for monotonic dual decomposition
International Journal of Approximate Reasoning
Message-passing algorithms for quadratic minimization
The Journal of Machine Learning Research
Variational algorithms for marginal MAP
The Journal of Machine Learning Research
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Message-passing algorithms have emerged as powerful techniques for approximate inference in graphical models. When these algorithms converge, they can be shown to find local (or sometimes even global) optima of variational formulations to the inference problem. But many of the most popular algorithms are not guaranteed to converge. This has lead to recent interest in convergent message-passing algorithms. In this paper, we present a unified view of convergent message-passing algorithms. We present a simple derivation of an abstract algorithm, tree-consistency bound optimization (TCBO) that is provably convergent in both its sum and max product forms. We then show that many of the existing convergent algorithms are instances of our TCBO algorithm, and obtain novel convergent algorithms "for free" by exchanging maximizations and summations in existing algorithms. In particular, we show that Wainwright's non-convergent sum-product algorithm for tree based variational bounds, is actually convergent with the right update order for the case where trees are monotonic chains.