Maximum Likelihood Reconstruction for Ising Models with Asynchronous Updates

    Phys. Rev. Lett. 110, 210601 – Published 20 May 2013
    Hong-Li Zeng, Mikko Alava, Erik Aurell, John Hertz, and Yasser Roudi

    Abstract

    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.

    DOI: http://dx.doi.org/10.1103/PhysRevLett.110.210601

    • Received 11 September 2012
    • Revised 26 November 2012
    • Published 20 May 2013

    © 2013 American Physical Society

    Authors & Affiliations

    Hong-Li Zeng1,*, Mikko Alava1, Erik Aurell2,3,4, John Hertz5,6, and Yasser Roudi5,7

    • 1Department of Applied Physics, Aalto University, FIN-00076 Aalto, Finland
    • 2Department of Computational Biology, KTH-Royal Institute of Technology, SE-100 44 Stockholm, Sweden
    • 3ACCESS Linnaeus Centre, KTH-Royal Institute of Technology, SE-100 44 Stockholm, Sweden
    • 4Department of Information and Computer Science, Aalto University, FIN-00076 Aalto, Finland
    • 5Nordita, KTH-Royal Institute of Technology and Stockholm University, 10691 Stockholm, Sweden
    • 6The Niels Bohr Institute, 2100 Copenhagen, Denmark
    • 7Kavli Institute for Systems Neuroscience, NTNU, 7030 Trondheim, Norway

    • *hong.zeng@aalto.fi

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