Reconstructing positive and negative couplings in Ising spin networks by sorted local transfer entropy

We employ the sorted local transfer entropy (SLTE) to reconstruct the coupling strengths of Ising spin networks with positive and negative couplings (J_{ij}), using only the time-series data of the spins. The SLTE method is model-free in the sense that no knowledge of the underlying dynamics of the spin system is required and is applicable to a broad class of systems. Contrary to the inference of coupling from pairwise transfer entropy, our method can reliably distinguish spin pair interactions with positive and negative couplings. The method is tested for the inverse Ising problem for different J_{ij} distributions and various spin dynamics, including synchronous and asynchronous update Glauber dynamics and Kawasaki exchange dynamics. It is found that the pairwise SLTE is proportional to the pairwise coupling strength to a good extent for all cases studied. In addition, the reconstruction works well for both the equilibrium and nonequilibrium cases of the time-series data. Comparison to other inverse Ising problem approaches using mean-field equations is also discussed.