Journal of Statistical Physics

, Volume 148, Issue 3, pp 502–512 | Cite as

Inference of Kinetic Ising Model on Sparse Graphs

  • Pan Zhang


Based on dynamical cavity method, we propose an approach to the inference of kinetic Ising model, which asks to reconstruct couplings and external fields from given time-dependent output of original system. Our approach gives an exact result on tree graphs and a good approximation on sparse graphs, it can be seen as an extension of Belief Propagation inference of static Ising model to kinetic Ising model. While existing mean field methods to the kinetic Ising inference e.g., naïve mean-field, TAP equation and simply mean-field, use approximations which calculate magnetizations and correlations at time t from statistics of data at time t−1, dynamical cavity method can use statistics of data at times earlier than t−1 to capture more correlations at different time steps. Extensive numerical experiments show that our inference method is superior to existing mean-field approaches on diluted networks.


Inverse Ising model Dynamical cavity method Bethe approximation 



The author would like to thank Abolfazl Ramezanpour and Riccardo Zecchina for discussing.


  1. 1.
    Cocco, S., Leibler, S., Monasson, R.: Proc. Natl. Acad. Sci. USA 206, 14058 (2009) ADSCrossRefGoogle Scholar
  2. 2.
    Weigt, M., White, R.A., Szurmant, H., Hoch, J.A., Hwa, T.: Proc. Natl. Acad. Sci. USA 106, 67 (2009) ADSCrossRefGoogle Scholar
  3. 3.
    Ackley, D.H., Hinton, G.E., Sejnowski, T.J.: Cogn. Sci. 9, 147 (1985). ISSN 0364-0213 CrossRefGoogle Scholar
  4. 4.
    Roudi, Y., Tyrcha, J., Hertz, J.: Phys. Rev. E 79, 051915 (2009) ADSCrossRefGoogle Scholar
  5. 5.
    Schneidman, E., Berry, M.J., Segev, R., Bialek, W.: Nature 440, 1007 (2006) ADSCrossRefGoogle Scholar
  6. 6.
    Roudi, Y., Hertz, J.: Phys. Rev. Lett. 106, 048702 (2011) ADSCrossRefGoogle Scholar
  7. 7.
    Mezard, M., Sakellariou, J.: J. Stat. Mech. 2011, L07001 (2011) CrossRefGoogle Scholar
  8. 8.
    Sakellariou, J., Roudi, Y., Mezard, M., Hertz, J.: arXiv:1106.0452 (2011)
  9. 9.
    Braunstein, A., Ramezanpour, A., Zecchina, R., Zhang, P.: Phys. Rev. E 83, 056114 (2011) ADSCrossRefGoogle Scholar
  10. 10.
    Zeng, H.-L., Aurell, E., Alava, M., Mahmoudi, H.: Phys. Rev. E 83, 041135 (2011) ADSCrossRefGoogle Scholar
  11. 11.
    Coolen, A.C.C.: arXiv:cond-mat/0006011 (2000)
  12. 12.
    Hatchett, J.P.L., Wemmenhove, B., Castillo, I.P., Nikoletopoulos, T., Skantzos, N.S., Coolen, A.C.C.: J. Phys. A, Math. Gen. 37, 6201 (2004) ADSzbMATHCrossRefGoogle Scholar
  13. 13.
    Coolen, A.C.C., Laughton, S.N., Sherrington, D.: Phys. Rev. B 53, 8184 (1996) ADSCrossRefGoogle Scholar
  14. 14.
    Sommers, H.-J.: Phys. Rev. Lett. 58, 1268 (1987) ADSCrossRefGoogle Scholar
  15. 15.
    Neri, I., Bolle, D.: J. Stat. Mech. 2009, P08009 (2009) CrossRefGoogle Scholar
  16. 16.
    Aurell, E., Mahmoudi, H.: J. Stat. Mech. 2011, P04014 (2011) CrossRefGoogle Scholar
  17. 17.
    Zhang, P., Chen, Y.: Physica A 387, 4441 (2008) ADSGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Politecnico di TorinoTorinoItaly

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