Dynamics and Performance of Susceptibility Propagation on Synthetic Data

TL;DR

This paper analyzes the Susceptibility Propagation algorithm's performance in solving the Inverse Ising problem, highlighting how temperature, connectivity, and magnetization affect its convergence and accuracy on synthetic data.

Contribution

It provides a detailed analysis of SusP's convergence behavior across temperature regimes and identifies factors influencing its effectiveness, including data quality and network properties.

Findings

High temperature (T>4) yields good performance.

Low temperature (T<4) causes divergence unless stopped early.

High connectivity and magnetization impair SusP performance.

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.