Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Numerical recipes in C (2nd ed.): the art of scientific computing
Numerical recipes in C (2nd ed.): the art of scientific computing
Natural gradient works efficiently in learning
Neural Computation
Learning in graphical models
Neural Computation
Information Geometry of Mean-Field Approximation
Neural Computation
Correctness of Local Probability Propagation in Graphical Models with Loops
Neural Computation
The geometry of turbo-decoding dynamics
IEEE Transactions on Information Theory
Information geometry on hierarchy of probability distributions
IEEE Transactions on Information Theory
Information geometry of turbo and low-density parity-check codes
IEEE Transactions on Information Theory
Integration of Stochastic Models by Minimizing α-Divergence
Neural Computation
On the Minima of Bethe Free Energy in Gaussian Distributions
ICAISC '08 Proceedings of the 9th international conference on Artificial Intelligence and Soft Computing
Information Geometry and Its Applications: Convex Function and Dually Flat Manifold
Emerging Trends in Visual Computing
Theoretical analysis of accuracy of Gaussian belief propagation
ICANN'07 Proceedings of the 17th international conference on Artificial neural networks
Convergent message passing algorithms: a unifying view
UAI '09 Proceedings of the Twenty-Fifth Conference on Uncertainty in Artificial Intelligence
Belief propagation, Dykstra's algorithm, and iterated information projections
IEEE Transactions on Information Theory
On the relationship between belief propagation decoding and joint maximum likelihood detection
IEEE Transactions on Communications
Dreaming of mathematical neuroscience for half a century
Neural Networks
Hi-index | 0.06 |
Belief propagation (BP) is a universal method of stochastic reasoning. It gives exact inference for stochastic models with tree interactions and works surprisingly well even if the models have loopy interactions. Its performance has been analyzed separately in many fields, such as AI, statistical physics, information theory, and information geometry. This article gives a unified framework for understanding BP and related methods and summarizes the results obtained in many fields. In particular, BP and its variants, including tree reparameterization and concave-convex procedure, are reformulated with information-geometrical terms, and their relations to the free energy function are elucidated from an information-geometrical viewpoint. We then propose a family of new algorithms. The stabilities of the algorithms are analyzed, and methods to accelerate them are investigated.