Impact of higher-order correlations on coincidence distributions of massively parallel data

The signature of neuronal assemblies is the higher-order correlation structure of the spiking activity of the participating neurons. Due to the rapid progress in recording technology the massively parallel data required to search for such signatures are now becoming available. However, existing statistical analysis tools are severely limited by the combinatorial explosion in the number of spike patterns to be considered. Therefore, population measaures need to be constructed reducing the number of tests and the recording time required, potentially for the price of being able to answer only a restricted set of questions. Here we investigate the population histogram of the time course of neuronal activity as the simplest example. The amplitude distribution of this histogram is called the complexity distribution. Independent of neuron identity it describes the probability to observe a particular number of synchronous spikes. On the basis of two models we illustrate that in the presence of higher-order correlations already the complexity distribution exhibits characteristic deviations from expectation. The distribution reflects the presence of correlation of a given order in the data near the corresponding complexity. However, depending on the details of the model also the regime of low complexities may be perturbed. In conclusion we propose that, for certain research questions, new statistical tools can overcome the problems caused by the combinatorial explosion in massively parallel recordings by evaluating features of the complexity distribution.