Advertisement

Optimizing Edge Weights for Distributed Inference with Gaussian Belief Propagation

  • Brendan Halloran
  • Prashan Premaratne
  • Peter James Vial
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10954)

Abstract

Distributed processing is becoming more important in robotics as low-cost ad hoc networks provide a scalable and robust alternative to tradition centralized processing. Gaussian belief propagation (GaBP) is an effective message-passing algorithm for performing inference on distributed networks, however, its accuracy and convergence can be significantly decreased as networks have higher connectivity and loops. This paper presents two empirically derived methods for weighting the messages in GaBP to minimize error. The first method uses uniform weights based on the average node degree across the network, and the second uses weights determined by the degrees of the nodes at either end of an edge. Extensive simulations show that this results in greatly decreased error, with even greater effects as the network scales. Finally, we present a practical application of this algorithm in the form of a multi-robot localization problem, with our weighting system improving the accuracy of the solution.

Keywords

Gaussian belief propagation Distributed algorithms Markov random fields Factor graphs Localization 

References

  1. 1.
    Pearl, J.: Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference, 2nd edn. Morgan Kaufmann, San Francisco (1988)zbMATHGoogle Scholar
  2. 2.
    Pearl, J.: Fusion, propagation, and structuring in belief networks. Artif. Intell. 29(3), 241–288 (1986)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Weiss, Y., Freeman, W.T.: Correctness of belief propagation in Gaussian graphical models of arbitrary topology. In: Advances in Neural Information Processing Systems, pp. 673–679 (2000)Google Scholar
  4. 4.
    Bickson, D.: Gaussian belief propagation: theory and application. arXiv preprint arXiv:0811.2518 (2008)
  5. 5.
    Yedidia, J.S., Freeman, W.T., Weiss, Y.: Generalized belief propagation. In: Advances in Neural Information Processing Systems, pp. 689–695 (2001)Google Scholar
  6. 6.
    Kschischang, F.R., Frey, B.J., Loeliger, H.A.: Factor graphs and the sum-product algorithm. IEEE Trans. Inf. Theor. 47(2), 498–519 (2001)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Sudderth, E.B., Ihler, A.T., Isard, M., Freeman, W.T., Willsky, A.S.: Nonparametric belief propagation. Commun. ACM 53(10), 95–103 (2010)CrossRefGoogle Scholar
  8. 8.
    Bickson, D., Yom-Tov, E., Dolev, D.: A gaussian belief propagation solver for large scale support vector machines. arXiv preprint arXiv:0810.1648 (2008)
  9. 9.
    Bickson, D., Dolev, D., Shental, O., Siegel, P.H., Wolf, J.K.: Gaussian belief propagation based multiuser detection. In: IEEE International Symposium on Information Theory, ISIT 2008, pp. 1878–1882. IEEE, July 2008Google Scholar
  10. 10.
    Bickson, D., Shental, O., Dolev, D.: Distributed Kalman filter via Gaussian belief propagation. In: 2008 46th Annual Allerton Conference on Communication, Control, and Computing, pp. 628–635. IEEE, September 2008Google Scholar
  11. 11.
    Shental, O., Bickson, D., Siegel, P.H., Wolf, J.K., Dolev, D.: Gaussian belief propagation for solving systems of linear equations: theory and application. arXiv preprint arXiv:0810.1119 (2008)
  12. 12.
    Halloran, B., Premaratne, P., Vial, P., Kadhim, I.: Distributed one dimensional calibration and localisation of a camera sensor network. In: Huang, D.-S., Jo, K.-H., Figueroa-García, J.C. (eds.) ICIC 2017. LNCS, vol. 10362, pp. 581–593. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-63312-1_51CrossRefGoogle Scholar
  13. 13.
    Savic, V., Zazo, S.: Cooperative localization in mobile networks using nonparametric variants of belief propagation. Ad Hoc Netw. 11(1), 138–150 (2013)CrossRefGoogle Scholar
  14. 14.
    Savic, V., Wymeersch, H.: Simultaneous localization and tracking via real-time nonparametric belief propagation. In: 2013 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 5180–5184. IEEE, May 2013Google Scholar
  15. 15.
    García-Fernández, Á.F., Svensson, L., Särkkä, S.: Cooperative localization using posterior linearization belief propagation. IEEE Trans. Veh. Technol. 67(1), 832–836 (2018)CrossRefGoogle Scholar
  16. 16.
    Hosseinidoust, Z., Giannacopoulos, D., Gross, W.J.: GPU optimization and implementation of Gaussian belief propagation algorithm. In: 2016 IEEE Conference on Electromagnetic Field Computation (CEFC). IEEE (2016)Google Scholar
  17. 17.
    El-Kurdi, Y., et al.: Acceleration of the finite-element gaussian belief propagation solver using minimum residual techniques. IEEE Trans. Magn. 52(3), 1–4 (2016)CrossRefGoogle Scholar
  18. 18.
    Yang, S., Premaratne, P., Vial, P.: Hand gesture recognition: an overview. In: 2013 5th IEEE International Conference on Broadband Network & Multimedia Technology (IC-BNMT). IEEE (2013)Google Scholar
  19. 19.
    Premaratne, P., Ajaz, S., Premaratne, M.: Hand gesture tracking and recognition system for control of consumer electronics. In: Huang, D.-S., Gan, Y., Gupta, P., Gromiha, M.M. (eds.) ICIC 2011. LNCS (LNAI), vol. 6839, pp. 588–593. Springer, Heidelberg (2012).  https://doi.org/10.1007/978-3-642-25944-9_76CrossRefGoogle Scholar
  20. 20.
    Du, J., Ma, S., Wu, Y.C., Kar, S., Moura, J.M.: Convergence analysis of distributed inference with vector-valued Gaussian belief propagation. arXiv preprint arXiv:1611.02010 (2016)
  21. 21.
    Du, J., Ma, S., Wu, Y.C., Kar, S., Moura, J.M.: Convergence analysis of the information matrix in Gaussian belief propagation. In: 2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 4074–4078. IEEE, March 2017Google Scholar
  22. 22.
    Wainwright, M.J., Jaakkola, T.S., Willsky, A.S.: Tree-reweighted belief propagation algorithms and approximate ML estimation by pseudo-moment matching. In: AISTATS, January 2003Google Scholar
  23. 23.
    Wymeersch, H., Penna, F., Savić, V.: Uniformly reweighted belief propagation: a factor graph approach. In: 2011 IEEE International Symposium on Information Theory Proceedings (ISIT), pp. 2000–2004. IEEE, July 2011Google Scholar
  24. 24.
    Savic, V., Wymeersch, H., Penna, F., Zazo, S.: Optimized edge appearance probability for cooperative localization based on tree-reweighted nonparametric belief propagation. In: 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 3028–3031. IEEE, May 2011Google Scholar
  25. 25.
    Watts, D.J., Strogatz, S.H.: Collective dynamics of ‘small-world’ networks. Nature 393(6684), 440 (1998)CrossRefGoogle Scholar
  26. 26.
    Cadena, C., Carlone, L., Carrillo, H., Latif, Y., Scaramuzza, D., Neira, J., Reid, I., Leonard, J.J.: Past, present, and future of simultaneous localization and mapping: Toward the robust-perception age. IEEE Trans. Rob. 32(6), 1309–1332 (2016)CrossRefGoogle Scholar
  27. 27.
    Meyer, F., et al.: Message passing algorithms for scalable multitarget tracking. Proc. IEEE 106(2), 221–259 (2018)CrossRefGoogle Scholar
  28. 28.
    Leitinger, E., et al.: A scalable belief propagation algorithm for radio signal based SLAM. arXiv preprint arXiv:1801.04463 (2018)

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Electrical, Computer and Telecommunication EngineeringUniversity of WollongongWollongongAustralia

Personalised recommendations