Dynamics and performance of susceptibility propagation on synthetic data
- 110 Downloads
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.
KeywordsSusceptibility Propagation Ising Model Belief Propagation Reconstruction Error Sparse Graph
Unable to display preview. Download preview PDF.
- 1.M. Mézard, A. Montanari, Information, Physics and Computation (Oxford University Press, 2009) Google Scholar
- 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.E. Marinari, V.V. Kerrebroeck, J. Stat. Mech. P02008 (2010) Google Scholar
- 15.C. Ollion, Susceptibility Propagation for the inverse Ising Problem (2010) Google Scholar
- 18.Y. Roudi, S. Nirenberg, P.E. Latham, PLoS Comp. Biol. 5, e1000380 (2009) Google Scholar