Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Approximate inference in Boltzmann machines
Artificial Intelligence
Expectation Propagation for approximate Bayesian inference
UAI '01 Proceedings of the 17th Conference in Uncertainty in Artificial Intelligence
Correctness of Local Probability Propagation in Graphical Models with Loops
Neural Computation
Loopy belief propagation for approximate inference: an empirical study
UAI'99 Proceedings of the Fifteenth conference on Uncertainty in artificial intelligence
Loopy belief propagation and Gibbs measures
UAI'02 Proceedings of the Eighteenth conference on Uncertainty in artificial intelligence
A new class of upper bounds on the log partition function
UAI'02 Proceedings of the Eighteenth conference on Uncertainty in artificial intelligence
Approximate inference and constrained optimization
UAI'03 Proceedings of the Nineteenth conference on Uncertainty in Artificial Intelligence
Factor graphs and the sum-product algorithm
IEEE Transactions on Information Theory
Turbo decoding as an instance of Pearl's “belief propagation” algorithm
IEEE Journal on Selected Areas in Communications
The Journal of Machine Learning Research
Efficient belief propagation for higher-order cliques using linear constraint nodes
Computer Vision and Image Understanding
On the Minima of Bethe Free Energy in Gaussian Distributions
ICAISC '08 Proceedings of the 9th international conference on Artificial Intelligence and Soft Computing
Graphical Models, Exponential Families, and Variational Inference
Foundations and Trends® in Machine Learning
Revealing the structure of medical dictations with conditional random fields
EMNLP '08 Proceedings of the Conference on Empirical Methods in Natural Language Processing
Convexity arguments for efficient minimization of the Bethe and Kikuchi free energies
Journal of Artificial Intelligence Research
Cortical circuitry implementing graphical models
Neural Computation
Nonparametric belief propagation
Communications of the ACM
Norm-product belief propagation: primal-dual message-passing for approximate inference
IEEE Transactions on Information Theory
Properties of Bethe free energies and message passing in Gaussian models
Journal of Artificial Intelligence Research
Applications of belief propagation in CSMA wireless networks
IEEE/ACM Transactions on Networking (TON)
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We derive sufficient conditions for the uniqueness of loopy belief propagation fixed points. These conditions depend on both the structure of the graph and the strength of the potentials and naturally extend those for convexity of the Bethe free energy. We compare them with (a strengthened version of) conditions derived elsewhere for pairwise potentials. We discuss possible implications for convergent algorithms, as well as for other approximate free energies.