Network inference using asynchronously updated kinetic Ising Model

TL;DR

This paper compares naive mean field and TAP approximations for reconstructing network structures from dynamical data in an asynchronous kinetic Ising model, analyzing the effects of temperature and data length on inference accuracy.

Contribution

It introduces two methods for TAP-based network inference and investigates their performance and temperature dependence in the asymmetric S-K model.

Findings

TAP outperforms nMF at low temperatures.

Convergence of the iteration method depends on the number of real roots of cubic equations.

Performance improves with longer data length.

Abstract

Network structures are reconstructed from dynamical data by respectively naive mean field (nMF) and Thouless-Anderson-Palmer (TAP) approximations. For TAP approximation, we use two methods to reconstruct the network: a) iteration method; b) casting the inference formula to a set of cubic equations and solving it directly. We investigate inference of the asymmetric Sherrington- Kirkpatrick (S-K) model using asynchronous update. The solutions of the sets cubic equation depend of temperature T in the S-K model, and a critical temperature Tc is found around 2.1. For T < Tc, the solutions of the cubic equation sets are composed of 1 real root and two conjugate complex roots while for T > Tc there are three real roots. The iteration method is convergent only if the cubic equations have three real solutions. The two methods give same results when the iteration method is convergent. Compared to nMF, TAP is somewhat better at low temperatures, but approaches the same performance as temperature increase. Both methods behave better for longer data length, but for improvement arises, TAP is well pronounced.