Eur. Phys. J. B 77, 587-595 (2010)
https://doi.org/10.1140/epjb/e2010-00277-0

Dynamics and performance of susceptibility propagation on synthetic data

¹ ACCESS Linnaeus Center KTH-Royal Institute of Technology, 100 44 Stockholm, Sweden
² Department of Informatics and Computer Science, Aalto University, FI-02015, Espoo, Finland
³ Department of Computational Biology, AlbaNova University Centre, 106 91 Stockholm, Sweden
⁴ NORDITA, Roslagstullsbacken 23, 10691 Stockholm, Sweden

Corresponding author: ^a yasser@nordita.org

Received: 21 May 2010
Revised: 24 August 2010
Published online: 22 September 2010

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.