On the effective implementation of the iterative proportional fitting procedure
Computational Statistics & Data Analysis - Special issue dedicated to Toma´sˇ Havra´nek
A view of the EM algorithm that justifies incremental, sparse, and other variants
Learning in graphical models
Loopy belief propagation and Gibbs measures
UAI'02 Proceedings of the Eighteenth conference on Uncertainty in artificial intelligence
On the uniqueness of loopy belief propagation fixed points
Neural Computation
Expectation Consistent Approximate Inference
The Journal of Machine Learning Research
Estimating the "Wrong" Graphical Model: Benefits in the Computation-Limited Setting
The Journal of Machine Learning Research
Loop Corrections for Approximate Inference on Factor Graphs
The Journal of Machine Learning Research
Efficient belief propagation for higher-order cliques using linear constraint nodes
Computer Vision and Image Understanding
Inference in the Promedas Medical Expert System
AIME '07 Proceedings of the 11th conference on Artificial Intelligence in Medicine
Graphical Models, Exponential Families, and Variational Inference
Foundations and Trends® in Machine Learning
Occlusion Boundaries from Motion: Low-Level Detection and Mid-Level Reasoning
International Journal of Computer Vision
Shape from Shading Using Probability Functions and Belief Propagation
International Journal of Computer Vision
Convexity arguments for efficient minimization of the Bethe and Kikuchi free energies
Journal of Artificial Intelligence Research
Graphical model inference in optimal control of stochastic multi-agent systems
Journal of Artificial Intelligence Research
Approximate inference on planar graphs using loop calculus and belief propagation
UAI '09 Proceedings of the Twenty-Fifth Conference on Uncertainty in Artificial Intelligence
Convexifying the Bethe free energy
UAI '09 Proceedings of the Twenty-Fifth Conference on Uncertainty in Artificial Intelligence
Approximate Inference on Planar Graphs using Loop Calculus and Belief Propagation
The Journal of Machine Learning Research
libDAI: A Free and Open Source C++ Library for Discrete Approximate Inference in Graphical Models
The Journal of Machine Learning Research
Recovering Occlusion Boundaries from an Image
International Journal of Computer Vision
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Loopy and generalized belief propagation are popular algorithms for approximate inference in Markov random fields and Bayesian networks. Fixed points of these algorithms correspond to extrema of the Bethe and Kikuchi free energy (Yedidia et al., 2001). However, belief propagation does not always converge, which motivates approaches that explicitly minimize the Kikuchi/Bethe free energy, such as CCCP (Yuille, 2002) and UPS (Teh and Welling, 2002). Here we describe a class of algorithms that solves this typically non-convex constrained minimization problem through a sequence of convex constrained minimizations of upper bounds on the Kikuchi free energy. Intuitively one would expect tighter bounds to lead to faster algorithms, which is indeed convincingly demonstrated in our simulations. Several ideas are applied to obtain tight convex bounds that yield dramatic speed-ups over CCCP.