Advertisement

The European Physical Journal B

, Volume 77, Issue 4, pp 587–595 | Cite as

Dynamics and performance of susceptibility propagation on synthetic data

  • E. Aurell
  • C. Ollion
  • Y. RoudiEmail author
Article

Abstract.

We study the performance and convergence properties of the susceptibility propagation (SusP) algorithm for solving the Inverse Ising problem. We first study how the temperature parameter (T) in a Sherrington-Kirkpatrick model generating the data influences the performance and convergence of the algorithm. We find that at the high temperature regime (T > 4), the algorithm performs well and its quality is only limited by the quality of the supplied data. In the low temperature regime (T < 4), we find that the algorithm typically does not converge, yielding diverging values for the couplings. However, we show that by stopping the algorithm at the right time before divergence becomes serious, good reconstruction can be achieved down to T 2. We then show that dense connectivity, loopiness of the connectivity, and high absolute magnetization all have deteriorating effects on the performance of the algorithm. When absolute magnetization is high, we show that other methods can be work better than SusP. Finally, we show that for neural data with high absolute magnetization, SusP performs less well than TAP inversion.

Keywords

Susceptibility Propagation Ising Model Belief Propagation Reconstruction Error Sparse Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    M. Mézard, A. Montanari, Information, Physics and Computation (Oxford University Press, 2009) Google Scholar
  2. 2.
    S. Cocco, S. Leibler, R. Monasson, Proc. Natl. Acad. Sci. USA 106, 14058 (2009) CrossRefADSGoogle Scholar
  3. 3.
    Y. Roudi, J.A. Hertz, E. Aurell, Front. Comput. Neurosci. 3, 22 (2009) CrossRefGoogle Scholar
  4. 4.
    Y. Roudi, J. Tyrcha, J. Hertz, Phys. Rev. E 79, 051915 (2009) CrossRefADSGoogle Scholar
  5. 5.
    E. Schneidman, M. Berry, R. Segev, W. Bialek, Nature 440, 1007 (2006) CrossRefADSGoogle Scholar
  6. 6.
    T.R. Lezon, J.R. Banavar, M. Cieplak, A. Maritan, N. Fedoroff, Proc. Natl. Acad. Sci. 103, 19033 (2006) CrossRefADSGoogle Scholar
  7. 7.
    D.H. Ackley, G.E. Hinton, T.J. Sejnowski, Cog. Sci. 9, 147 (1985) CrossRefGoogle Scholar
  8. 8.
    H.J. Kappen, F.B. Rodriguez, Neur. Comp. 10, 1137 (1998) CrossRefGoogle Scholar
  9. 9.
    T. Tanaka, Phys. Rev. E 58, 2302 (1998) CrossRefADSGoogle Scholar
  10. 10.
    V. Sessak, R. Monasson, J. Phys. A: Math. Theor. 42, 1 (2009) CrossRefMathSciNetGoogle Scholar
  11. 11.
    P. Ravikumar, M. Wainwright, J.D. Lafferty, Ann. Stat. 38, 1287 (2010) zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    M. Mézard, T. Mora, J. Physiol. Paris 103, 107 (2009) CrossRefGoogle Scholar
  13. 13.
    J.S. Yedidia, W.T. Freeman, Y. Weiss, Understanding Belief Propagation and its Generalizations (Science & Technology Books, 2003), pp. 239–269 Google Scholar
  14. 14.
    E. Marinari, V.V. Kerrebroeck, J. Stat. Mech. P02008 (2010) Google Scholar
  15. 15.
    C. Ollion, Susceptibility Propagation for the inverse Ising Problem (2010) Google Scholar
  16. 16.
    D. Sherrington, S. Kirkpatrick, Phys. Rev. Lett. 35, 1792 (1975) CrossRefADSGoogle Scholar
  17. 17.
    J. Shlens, G. Field, J. Gauthier, M. Grivich, D. Petrusca, A. Sher, A. Litke, E. Chichilnisky, J. Neurosci. 26, 8254 (2006) CrossRefGoogle Scholar
  18. 18.
    Y. Roudi, S. Nirenberg, P.E. Latham, PLoS Comp. Biol. 5, e1000380 (2009) Google Scholar
  19. 19.
    J.M. Mooij, H.J. Kappen, J. Mach. Learn. Res. 8, 1113 (2007) MathSciNetGoogle Scholar
  20. 20.
    M. Weigt, R.A. White, H. Szurmant, J.A. Hoch, T. Hwa, PNAS 106, 67 (2009) CrossRefADSGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.ACCESS Linnaeus Center KTH-Royal Institute of TechnologyStockholmSweden
  2. 2.Department of Informatics and Computer ScienceAalto UniversityEspooFinland
  3. 3.Department of Computational BiologyAlbaNova University CentreStockholmSweden
  4. 4.NORDITA, Roslagstullsbacken 23StockholmSweden

Personalised recommendations