Science China Information Sciences

, 61:092202 | Cite as

Distributed regression estimation with incomplete data in multi-agent networks

Research Paper
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Abstract

In this paper, distributed regression estimation problem with incomplete data in a time-varying multi-agent network is investigated. Regression estimation is carried out based on local agent information with incomplete in the non-ignorable mechanism. By virtue of gradient-based design and adaptive filter, a distributed algorithm is proposed to deal with a regression estimation problem with incomplete data. With the help of convex analysis and stochastic approximation techniques, the exact convergence is obtained for the proposed algorithm with incomplete data and a jointly-connected multi-agent topology. Moreover, online regret analysis is also given for real-time learning. Then, simulations for the proposed algorithm are also given to demonstrate how it can solve the estimation problem in a distributed way, even when the network configuration is time-varying.

Keywords

multi-agent systems time-varying network estimation with incomplete data online learning stochastic approximation 

Notes

Acknowledgements

This work was supported by National Key Research and Development Program of China (Grant No. 2016YFB0901902) and National Natural Science Foundation of China (Grant Nos. 61573344, 61333001, 61374168).

References

  1. 1.
    Nedić A, Ozdaglar A. Distributed subgradient methods for multi-agent optimization. IEEE Trans Automat Control, 2009, 54: 48–61MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Shi G, Johansson K. Robust consensus for continuous-time multiagent dynamics. SIAM J Control Optim, 2013, 51: 3673–3691MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Zhang Y Q, Lou Y C, Hong Y G, et al. Distributed projection-based algorithms for source localization in wireless sensor networks. IEEE Trans Wirel Commun, 2015, 43: 3131–3142CrossRefGoogle Scholar
  4. 4.
    Feng H, Jiang Z D, Hu B, et al. The incremental subgradient methods on distributed estimations in-network. Sci China Inf Sci, 2014, 57: 092103Google Scholar
  5. 5.
    Lou Y C, Hong Y G, Wang S Y. Distributed continuous-time approximate projection protocols for shortest distance optimization problems. Automatica, 2016, 69: 289–297MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Yi P, Hong Y G, Liu F. Initialization-free distributed algorithms for optimal resource allocation with feasibility con-straints and application to economic dispatch of power systems. Automatica, 2016, 74: 259–269MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Kokaram A C. On missing data treatment for degraded video and film archives: a survey and a new Bayesian approach. IEEE Trans Image Process, 2004, 13: 397–415CrossRefGoogle Scholar
  8. 8.
    Molenberghs G, Kenward M G. Missing Data in Clinical Studies. New York: Wiley, 2007CrossRefGoogle Scholar
  9. 9.
    Ibrahim J G, Chen M H, Lipsitz S R, et al. Missing data methods for generalized linear models: a comparative review. J Am Stat Assoc, 2005, 100: 332–346MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Gholami M R, Jansson M, Strom E G, et al. Diffusion estimation over cooperative multi-agent networks with missing data. IEEE Trans Signal Inf Process Netw, 2016, 2: 276–289MathSciNetCrossRefGoogle Scholar
  11. 11.
    Davey A, Savla J. Statistical Power Analysis with Missing Data: A Structural Equation Modeling Approach. Oxford, UK: Routledge Academic, 2009Google Scholar
  12. 12.
    Ram S S, Nedić A, Veeravalli V V. Distributed stochastic subgradient projection algorithms for convex optimization. J Optim Theory Appl, 2010, 147: 516–545MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Graybill F, Iyer H K. Regression Analysis: Concepts and Applications. California: Duxbury Press Belmont, 1994MATHGoogle Scholar
  14. 14.
    Feng Y, Sundaram S, Vishwanathan S V N, et al. Distributed autonomous online learning: regrets and intrinsic privacy-preserving properties. IEEE Trans Knowl Data Eng, 2013, 25: 2483–2493CrossRefGoogle Scholar
  15. 15.
    Hazan E, Kale S. Beyond the regret minimization barrier: optimal algorithms for stochastic strongly-convex optimiza-tion. J Mach Learn Res, 2014, 15: 2489–2512MathSciNetMATHGoogle Scholar
  16. 16.
    Shamir O, Zhang T. Stochastic gradient descent for non-smooth optimization: convergence results and optimal aver-aging schemes. In: Proceedings of International Conference on Machine Learning, Edinburgh, 2012. 71–79Google Scholar
  17. 17.
    Towfic Z J, Chen J S, Sayed A H. On distributed online classification in the midst of concept drifts. Neurocomputing, 2013, 112: 138–152CrossRefGoogle Scholar
  18. 18.
    Widrow B, Stearns S D. Adaptive Signal Processing. Cliffs: Prentice-Hall, 1985. 1–32MATHGoogle Scholar
  19. 19.
    Sayed A H. Adaptation, learning, and optimization over networks. Found Trends Mach Learn, 2014, 7: 311–801CrossRefMATHGoogle Scholar
  20. 20.
    Sayed A H, Tu S Y, Chen J S, et al. Diffusion strategies for adaptation and learning. IEEE Signal Proc Mag, 2013, 30: 155–171CrossRefGoogle Scholar
  21. 21.
    Polyak B T. Introduction to Optimization. New York: Optimization Software Inc., 1983. 2–8Google Scholar
  22. 22.
    Godsil C, Royle G. Algebraic Graph Theory. New York: Springer-Verlag, 2001. 1–18MATHGoogle Scholar
  23. 23.
    Ferguson T S. A Course in Large Sample Theory. London: Chapman and Hall Ltd., 1996. 3–4CrossRefMATHGoogle Scholar
  24. 24.
    Durrett R. Probability Theory and Examples. Camberidge, UK: Camberidge Press, 2010. 328–347CrossRefMATHGoogle Scholar
  25. 25.
    Enders C K. Applied Missing Data Analysis. New York: The Guilford Press, 2010Google Scholar
  26. 26.
    Kushner H J, Yin G. Stochastic Approximation and Recursive Algorithms and Applications. New York: Springer-Verlag, 1997. 117–157CrossRefGoogle Scholar
  27. 27.
    Widrow B, Mccool J, Larimore M G, et al. Stationary and nonstationary learning characteristics of the LMS adaptive filter. Proc IEEE, 1976, 64: 1151–1162MathSciNetCrossRefGoogle Scholar
  28. 28.
    Yi P, Hong Y G. Stochastic sub-gradient algorithm for distributed optimization with random sleep scheme. Control Theory Technol, 2015, 13: 333–347MathSciNetCrossRefMATHGoogle Scholar
  29. 29.
    Larsen R J, Max M L. An Introduction to Mathematical Statistics and Its Applications. 4th ed. New York: Pearson, 2006. 221–280Google Scholar

Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.University of Chinese Academy of SciencesBeijingChina
  2. 2.Key Laboratory of Systems and Control, Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijingChina

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