Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Graphical models for machine learning and digital communication
Graphical models for machine learning and digital communication
The Handbook of Brain Theory and Neural Networks
The Handbook of Brain Theory and Neural Networks
Pattern Recognition and Neural Networks
Pattern Recognition and Neural Networks
Neural Computation
ICCV '99 Proceedings of the International Conference on Computer Vision-Volume 2 - Volume 2
Flows suspending iterative algorithms
Flows suspending iterative algorithms
Correctness of Local Probability Propagation in Graphical Models with Loops
Neural Computation
A novel optimizing network architecture with applications
Neural Computation
Neural Computation
Mean field theory for sigmoid belief networks
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
Turbo decoding as an instance of Pearl's “belief propagation” algorithm
IEEE Journal on Selected Areas in Communications
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Recent work (Yedidia, Freeman, Weiss [22]) has shown that stable points of belief propagation (BP) algorithms [12] for graphs with loops correspond to extrema of the Bethe free energy [3]. These BP algorithms have been used to obtain good solutions to problems for which alternative algorithms fail to work [4], [5], [10] [11]. In this paper we introduce a discrete iterative algorithm which we prove is guaranteed to converge to a minimum of the Bethe free energy. We call this the double-loop algorithm because it contains an inner and an outer loop. The algorithm is developed by decomposing the free energy into a convex part and a concave part, see [25], and extends a class of mean field theory algorithms developed by [7], [8] and, in particular, [13]. Moreover, the double-loop algorithm is formally very similar to BP which may help understand when BP converges. In related work [24] we extend this work to the more general Kikuchi approximation [3] which includes the Bethe free energy as a special case. It is anticipated that these double-loop algorithms will be useful for solving optimization problems in computer vision and other applications.