A study of dependency features of spike trains through copulas

Despite the progresses of statistical and machine learning techniques, simultaneous recordings from many neurons hide important information and the connections characterizing the network remain generally undiscovered. Discerning the presence of direct links between neurons from data is still a not completely solved problem. We propose the use of copulas, to enlarge the number of tools for detecting the network structure, pursuing on a research direction we started in Sacerdote et al. (2012). Here, our aim is to distinguish different types of connections on a very simple network. Our proposal consists in choosing suitable random intervals in pairs of spike trains determining the shapes of their copulas. We show that this approach allows to detect different types of dependencies. We illustrate the features of the proposed method on synthetic data from suitably connected networks of two or three formal neurons directly connected or influenced by the surrounding network. We show how a smart choice of pairs of random times together with the use of empirical copulas allows to discern between direct and indirect interactions.