Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
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 uniqueness of loopy belief propagation fixed points
Neural Computation
Change Point Problems in Linear Dynamical Systems
The Journal of Machine Learning Research
Walk-Sums and Belief Propagation in Gaussian Graphical Models
The Journal of Machine Learning Research
Bayesian Inference and Optimal Design for the Sparse Linear Model
The Journal of Machine Learning Research
Accuracy of Loopy belief propagation in Gaussian models
Neural Networks
Fixing convergence of Gaussian belief propagation
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 3
Loopy belief propagation for approximate inference: an empirical study
UAI'99 Proceedings of the Fifteenth conference on Uncertainty in artificial intelligence
An analysis of belief propagation on the turbo decoding graph with Gaussian densities
IEEE Transactions on Information Theory
Matrix Analysis
Robust Gaussian Process Regression with a Student-t Likelihood
The Journal of Machine Learning Research
Approximating the permanent with fractional belief propagation
The Journal of Machine Learning Research
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We address the problem of computing approximate marginals in Gaussian probabilistic models by using mean field and fractional Bethe approximations. We define the Gaussian fractional Bethe free energy in terms of the moment parameters of the approximate marginals, derive a lower and an upper bound on the fractional Bethe free energy and establish a necessary condition for the lower bound to be bounded from below. It turns out that the condition is identical to the pairwise normalizability condition, which is known to be a sufficient condition for the convergence of the message passing algorithm. We show that stable fixed points of the Gaussian message passing algorithm are local minima of the Gaussian Bethe free energy. By a counterexample, we disprove the conjecture stating that the unboundedness of the free energy implies the divergence of the message passing algorithm.