  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
$\ell_1$-optimization 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 widely-used $\ell
_1$-optimization based methods.
