The volume of relaxed Boolean-quadric and cut polytopes
Discrete Mathematics
An introduction to variational methods for graphical models
Learning in graphical models
Belief Optimization for Binary Networks: A Stable Alternative to Loopy Belief Propagation
UAI '01 Proceedings of the 17th Conference in Uncertainty in Artificial Intelligence
On the choice of regions for generalized belief propagation
UAI '04 Proceedings of the 20th conference on Uncertainty in artificial intelligence
Estimation and Marginalization Using the Kikuchi Approximation Methods
Neural Computation
Estimating the "Wrong" Graphical Model: Benefits in the Computation-Limited Setting
The Journal of Machine Learning Research
Graphical Models, Exponential Families, and Variational Inference
Foundations and Trends® in Machine Learning
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
Approximate inference and constrained optimization
UAI'03 Proceedings of the Nineteenth 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
FastInf: An Efficient Approximate Inference Library
The Journal of Machine Learning Research
Norm-product belief propagation: primal-dual message-passing for approximate inference
IEEE Transactions on Information Theory
Recursive sum-product algorithm for generalized outer-planar graphs
Information Processing Letters
Decomposition and Approximation of Loopy Bayesian Networks
Fundamenta Informaticae
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The introduction of loopy belief propagation (LBP) revitalized the application of graphical models in many domains. Many recent works present improvements on the basic LBP algorithm in an attempt to overcome convergence and local optima problems. Notable among these are convexified free energy approximations that lead to inference procedures with provable convergence and quality properties. However, empirically LBP still outperforms most of its convex variants in a variety of settings, as we also demonstrate here. Motivated by this fact we seek convexified free energies that directly approximate the Bethe free energy. We show that the proposed approximations compare favorably with state-of-the art convex free energy approximations.