Maximum Likelihood Reconstruction for Ising Models with Asynchronous Updates

Hong-Li Zeng; Mikko Alava; Erik Aurell; John Hertz; Yasser Roudi

doi:10.1103/PhysRevLett.110.210601

Maximum Likelihood Reconstruction for Ising Models with Asynchronous Updates

Hong-Li Zeng, Mikko Alava, Erik Aurell, John Hertz, Yasser Roudi

Biocomplexity

22 Citations (Scopus)

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.

Original language	English
Article number	210601
Journal	Physical Review Letters
Volume	110
Issue number	21
ISSN	0031-9007
DOIs	https://doi.org/10.1103/PhysRevLett.110.210601
Publication status	Published - 20 May 2013

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title = "Maximum Likelihood Reconstruction for Ising Models with Asynchronous Updates",

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.",

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AU - Zeng, Hong-Li

AU - Alava, Mikko

AU - Aurell, Erik

AU - Hertz, John

AU - Roudi, Yasser

PY - 2013/5/20

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N2 - 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.

AB - 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.

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Maximum Likelihood Reconstruction for Ising Models with Asynchronous Updates

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