Matrix analysis
Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Parallel and Distributed Computation: Numerical Methods
Parallel and Distributed Computation: Numerical Methods
Walk-Sums and Belief Propagation in Gaussian Graphical Models
The Journal of Machine Learning Research
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
Convergence of min-sum message-passing for convex optimization
IEEE Transactions on Information Theory
An analysis of belief propagation on the turbo decoding graph with Gaussian densities
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Distributed Node-Specific LCMV Beamforming in Wireless Sensor Networks
IEEE Transactions on Signal Processing
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In this letter, we propose a new message-passing algorithm for quadratic optimization. The design of the new algorithm is based on linear coordinate descent between neighboring nodes. The updating messages are in a form of linear functions as compared to the min-sum algorithm of which the messages are in a form of quadratic functions. As a result, the linear coordinate-descent (LiCD) algorithm transmits only one parameter per message as opposed to the min-sum algorithm, which transmits two parameters per message. We show that when the quadratic matrix is walk-summable, the LiCD algorithm converges. By taking the LiCD algorithm as a subroutine, we also fix the convergence issue for a general quadratic matrix. The LiCD algorithm works in either a synchronous or asynchronous message-passing manner. Experimental results show that for a general graph with multiple cycles, the LiCD algorithm has comparable convergence speed to the min-sum algorithm, thereby reducing the number of parameters to be transmitted and the computational complexity.