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In this paper we study the inference of the kinetic Ising model on sparsegraphs by the decimation method. The decimation method, which was firstproposed in [Phys. Rev. Lett. 112, 070603] for the static inverse Isingproblem, tries to recover the topology of the inferred system by setting theweakest couplings to zero iteratively. During the decimation process thelikelihood function is maximized over the remaining couplings. Unlike the$\ell_1$-optimization based methods, the decimation method does not use theLaplace distribution as a heuristic choice of prior to select a sparsesolution. In our case, the whole process can be done automatically withoutfixing 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 thedata, the decimation process can be applied naturally into a maximum-likelihoodoptimization algorithm, as opposed to the static case where pseudo-likelihoodmethod needs to be adopted. We also use extensive numerical studies to validatethe accuracy of our methods in dynamical inference problems. Our resultsillustrate that on various topologies and with different distribution ofcouplings, the decimation method outperforms the widely-used $\ell_1$-optimization based methods.

Inference of the sparse kinetic Ising model using the decimation method