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Convergence of Min-Sum-Min Message-Passing for Quadratic Optimization

  • Guoqiang Zhang
  • Richard Heusdens
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8726)

Abstract

We propose a new message-passing algorithm for the quadratic optimization problem. As opposed to the min-sum algorithm, the new algorithm involves two minimizations and one summation at each iteration. The new min-sum-min algorithm exploits feedback from last iteration in generating new messages, resembling the Jacobi- relaxation algorithm. We show that if the feedback signal is large enough, the min-sum-min algorithm is guaranteed to converge to the optimal solution. Experimental results show that the min-sum-min algorithm outperforms two reference methods w.r.t. the convergence speed.

Keywords

quadratic optimization Gaussian belief propagation min-sum min-sum-min 

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References

  1. 1.
    Bertsekas, D.P., Tsitsikis, J.N.: Parallel and distributed Computation: Numerical Methods. Athena Scientific, Belmont (1997)Google Scholar
  2. 2.
    Bishop, C.M.: Pattern Recognition and Machine Learning. Springer (2007)Google Scholar
  3. 3.
    Johnson, J.K., Malioutov, D.M., Willsky, A.S.: Walk-sum Interpretation and Analysis of Gaussian Belief Propagation. In: Advances in Neural Information Processing Systems, vol. 18. MIT Press, Cambridge (2006)Google Scholar
  4. 4.
    Johnson, J.K., Bickson, D., Dolev, D.: Fixing Convergence of Gaussian Belief Propagation. In: The International Symposium on Information Theory (2009)Google Scholar
  5. 5.
    Malioutov, D.M., Johnson, J.K., Willsky, A.S.: Walk-Sums and Belief Propagation in Gaussian Graphical Models. J. Mach. Learn. Res. 7, 2031–2064 (2006)zbMATHMathSciNetGoogle Scholar
  6. 6.
    Moallemi, C.C., Van Roy, B.: Convergence of Min-Sum Message Passing for Quadratic Optimization. IEEE Trans. Inf. Theory 55(5), 2413–2423 (2009)CrossRefGoogle Scholar
  7. 7.
    Moallemi, C.C., Van Roy, B.: Convergence of Min-Sum Message Passing for Convex Optimization. IEEE Trans. Inf. Theory 56(4), 2041–2050 (2010)CrossRefGoogle Scholar
  8. 8.
    Pearl, J.: Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufman Publishers (1988)Google Scholar
  9. 9.
    Zhang, G., Heusdens, R.: Linear Coordinate-Descent Message-Passing for Quadratic Optimization. Neural Computation 24(12), 3340–3370 (2012)CrossRefzbMATHMathSciNetGoogle Scholar
  10. 10.
    Zhang, G., Heusdens, R.: Convergence of Generalized Linear Coordinate-Descent Message-Passing for Quadratic Optimization. In: IEEE International Symposium on Information Theory Proceedings, pp. 1997–2001 (2012)Google Scholar
  11. 11.
    Matrix Market: Harwell Boeing Collection, http://math.nist.gov/MatrixMarket/index.html

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Guoqiang Zhang
    • 1
  • Richard Heusdens
    • 1
  1. 1.Department of Circuits and SystemsDelft University of TechnologyDelftThe Netherlands

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