Maximum Likelihood Reconstruction for Ising Models with Asynchronous Updates

作     者：Hong-Li Zeng Mikko Alava Erik Aurell John Hertz Yasser Roudi 

作者机构：Department of Applied Physics Aalto University FIN-00076 Aalto Finland Department of Computational Biology KTH-Royal Institute of Technology SE-100 44 Stockholm Sweden ACCESS Linnaeus Centre KTH-Royal Institute of Technology SE-100 44 Stockholm Sweden Department of Information and Computer Science Aalto University FIN-00076 Aalto Finland Nordita KTH-Royal Institute of Technology and Stockholm University 10691 Stockholm Sweden The Niels Bohr Institute 2100 Copenhagen Denmark Kavli Institute for Systems Neuroscience NTNU 7030 Trondheim Norway 

出 版 物：《Physical Review Letters》 (Phys Rev Lett)

年 卷 期：2013年第110卷第21期

页      面：210601-210601页

核心收录：

学科分类：07[理学] 0702[理学-物理学] 

基　　金：Finnish graduate school for Computational Science (FICS) Academy of Finland as part of its Finland Distinguished Professor program project [129024/Aurell] Center of Excellence COMP Center of Excellence COIN Center of Excellence NORDITA Kavli Foundation 

主　　题：MAGNETIC couplings ISING model ASYNCHRONOUS circuits DECOUPLING (Mathematics) EQUATIONS MOTION 

摘      要：We describe how the couplings in an asynchronous kinetic Ising model can be inferred. We consider two cases: one in which we know both the spin history and the update times and one in which we know only the spin history. For the first case, we show that one can average over all possible choices of update times to obtain a learning rule that depends only on spin correlations and can also be derived from the equations of motion for the correlations. For the second case, the same rule can be derived within a further decoupling approximation. We study all methods numerically for fully asymmetric Sherrington-Kirkpatrick models, varying the data length, system size, temperature, and external field. Good convergence is observed in accordance with the theoretical expectations.