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Recent remarkable advances in the experimental techniques have provided abackground for inferring neuronal couplings from point process data thatincludes a great number of neurons. Here, we propose a systematic procedure forpre- and post-processing generic point process data in an objective manner, tohandle data in the framework of a binary simple statistical model, the Ising orgeneralized McCulloch--Pitts model. The procedure involves two steps: (1)determining time-bin size for transforming the point-process data intodiscrete-time binary data and (2) screening relevant couplings from theestimated couplings. For the first step, we decide the optimal time-bin size byintroducing the null hypothesis that all neurons would fire independently, thenchoosing a time-bin size so that the null hypothesis is rejected with the moststrict criterion. The likelihood associated with the null hypothesis isanalytically evaluated and used for the rejection process. For the secondpost-processing step, after a certain estimator of coupling is obtained basedon the pre-processed dataset, the estimate is compared with many otherestimates derived from datasets obtained by randomizing the original dataset inthe time direction. We accept the original estimate as relevant only if itsabsolute value is sufficiently larger than them of randomized datasets. Thesemanipulations suppress false positive couplings induced by statistical noise.We apply this inference procedure to spiking data from synthetic and in vitroneuronal networks. The results show that the proposed procedure identifies thepresence/absence of synaptic couplings fairly well including their signs, forthe synthetic and experimental data. In particular, the results support that wecan infer the physical connections of underlying systems in favorablesituations, even when using the simple statistical model.

Inferring neuronal couplings from spiking data using a systematic procedure with a statistical criterion