Department of Physics and Center for Complex Systems, National Central University, Chung-Li District, Taoyuan City 320, Taiwan, Republic of China and Molecular Science and Technology Program, Taiwan International Graduate Program, Academia Sinica, Taipei, Taiwan, Republic of China.
Phys Rev E. 2019 Jul;100(1-1):012121. doi: 10.1103/PhysRevE.100.012121.
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.
我们使用排序局部转移熵 (SLTE) 仅通过自旋的时间序列数据来重建具有正、负耦合 (J_{ij}) 的伊辛自旋网络的耦合强度。SLTE 方法是无模型的，因为它不需要了解自旋系统的潜在动力学，并且适用于广泛的系统类别。与从成对转移熵推断耦合相反，我们的方法可以可靠地区分具有正、负耦合的自旋对相互作用。该方法针对不同的 J_{ij} 分布和各种自旋动力学（包括同步和异步更新的玻尔兹曼动力学和卡瓦萨基交换动力学）对逆伊辛问题进行了测试。结果发现，对于所有研究的情况，成对的 SLTE 在很大程度上与成对耦合强度成正比。此外，该重建方法在时间序列数据的平衡和非平衡情况下都能很好地工作。还讨论了与使用平均场方程的其他逆伊辛问题方法的比较。
