Matrix analysis
Topics in matrix analysis
Probabilistic Networks and Expert Systems
Probabilistic Networks and Expert Systems
Understanding belief propagation and its generalizations
Exploring artificial intelligence in the new millennium
Loopy Belief Propagation: Convergence and Effects of Message Errors
The Journal of Machine Learning Research
Loopy belief propagation and Gibbs measures
UAI'02 Proceedings of the Eighteenth conference on Uncertainty in artificial intelligence
Embedded trees: estimation of Gaussian Processes on graphs with cycles
IEEE Transactions on Signal Processing
An analysis of belief propagation on the turbo decoding graph with Gaussian densities
IEEE Transactions on Information Theory
Tree-based reparameterization framework for analysis of sum-product and related algorithms
IEEE Transactions on Information Theory
Graphical Models, Exponential Families, and Variational Inference
Foundations and Trends® in Machine Learning
Orbit-product representation and correction of Gaussian belief propagation
ICML '09 Proceedings of the 26th Annual International Conference on Machine Learning
Convergence of min-sum message passing for quadratic optimization
IEEE Transactions on Information Theory
Fixing convergence of Gaussian belief propagation
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 3
Distributed large scale network utility maximization
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 2
Covariance estimation in decomposable Gaussian graphical models
IEEE Transactions on Signal Processing
A low density lattice decoder via non-parametric belief propagation
Allerton'09 Proceedings of the 47th annual Allerton conference on Communication, control, and computing
Graph covers and quadratic minimization
Allerton'09 Proceedings of the 47th annual Allerton conference on Communication, control, and computing
Convergence of min-sum message-passing for convex optimization
IEEE Transactions on Information Theory
Distributed averaging via lifted Markov chains
IEEE Transactions on Information Theory
Poisonedwater: An improved approach for accurate reputation ranking in P2P networks
Future Generation Computer Systems
Belief propagation for min-cost network flow: convergence & correctness
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Resource Allocation via Message Passing
INFORMS Journal on Computing
SAMT'10 Proceedings of the 5th international conference on Semantic and digital media technologies
Unifying guilt-by-association approaches: theorems and fast algorithms
ECML PKDD'11 Proceedings of the 2011 European conference on Machine learning and knowledge discovery in databases - Volume Part II
Properties of Bethe free energies and message passing in Gaussian models
Journal of Artificial Intelligence Research
Belief Propagation for Min-Cost Network Flow: Convergence and Correctness
Operations Research
Graph-based distributed cooperative navigation for a general multi-robot measurement model
International Journal of Robotics Research
Resource Allocation via Message Passing
INFORMS Journal on Computing
Linear coordinate-descent message passing for quadratic optimization
Neural Computation
Collective inference for network data with copula latent markov networks
Proceedings of the sixth ACM international conference on Web search and data mining
High-dimensional Gaussian graphical model selection: walk summability and local separation criterion
The Journal of Machine Learning Research
Message-passing algorithms for quadratic minimization
The Journal of Machine Learning Research
Estimating scene flow using an interconnected patch surface model with belief-propagation inference
Computer Vision and Image Understanding
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We present a new framework based on walks in a graph for analysis and inference in Gaussian graphical models. The key idea is to decompose the correlation between each pair of variables as a sum over all walks between those variables in the graph. The weight of each walk is given by a product of edgewise partial correlation coefficients. This representation holds for a large class of Gaussian graphical models which we call walk-summable. We give a precise characterization of this class of models, and relate it to other classes including diagonally dominant, attractive, non-frustrated, and pairwise-normalizable. We provide a walk-sum interpretation of Gaussian belief propagation in trees and of the approximate method of loopy belief propagation in graphs with cycles. The walk-sum perspective leads to a better understanding of Gaussian belief propagation and to stronger results for its convergence in loopy graphs.