Inference of the sparse kinetic Ising model using the decimation method

Aurélien Decelle 1, 2, 3 Pan Zhang 4, 5
2 TAO - Machine Learning and Optimisation
LRI - Laboratoire de Recherche en Informatique, UP11 - Université Paris-Sud - Paris 11, Inria Saclay - Ile de France, CNRS - Centre National de la Recherche Scientifique : UMR8623
Abstract : In this paper we study the inference of the kinetic Ising model on sparse graphs by the decimation method. The decimation method, which was first proposed in [Phys. Rev. Lett. 112, 070603] for the static inverse Ising problem, tries to recover the topology of the inferred system by setting the weakest couplings to zero iteratively. During the decimation process the likelihood function is maximized over the remaining couplings. Unlike the based methods, the decimation method does not use the Laplace distribution as a heuristic choice of prior to select a sparse solution. In our case, the whole process can be done automatically without fixing any parameters by hand. We show that in the dynamical inference problem, where the task is to reconstruct the couplings of an Ising model given the data, the decimation process can be applied naturally into a maximum-likelihood optimization algorithm, as opposed to the static case where pseudo-likelihood method needs to be adopted. We also use extensive numerical studies to validate the accuracy of our methods in dynamical inference problems. Our results illustrate that on various topologies and with different distribution of couplings, the decimation method outperforms the l1-optimization widely-used based methods.
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Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, American Physical Society, 2015, Physical Review E, 91 (5), 〈http://journals.aps.org/pre/〉. 〈10.1103/PhysRevE.91.052136〉
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Aurélien Decelle, Pan Zhang. Inference of the sparse kinetic Ising model using the decimation method. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, American Physical Society, 2015, Physical Review E, 91 (5), 〈http://journals.aps.org/pre/〉. 〈10.1103/PhysRevE.91.052136〉. 〈hal-01250830〉

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