ACE: A Novel Approach for the Statistical Analysis of Pairwise Connectivity

Analysing correlations between streams of events is an important problem. It arises for example in Neurosciences, when the connectivity of neurons should be inferred from spike trains that record neurons' individual spiking activity. While recently some approaches for inferring delayed synaptic connections have been proposed, they are limited in the types of connectivities and delays they are able to handle, or require computation-intensive procedures. This paper proposes a faster and more flexible approach for analysing such delayed correlated activity: a statistical approach for the Analysis of Connectivity in spiking Events (ACE), based on the idea of hypothesis testing. It first computes for any pair of a source and a target neuron the inter-spike delays between subsequent source- and target-spikes. Then, it derives a null model for the distribution of inter-spike delays for \emph{uncorrelated}~neurons. Finally, it compares the observed distribution of inter-spike delays to this null model and infers pairwise connectivity based on the Pearson's Chi-squared test statistic. Thus, ACE is capable to detect connections with a priori unknown, non-discrete (and potentially large) inter-spike delays, which might vary between pairs of neurons. Since ACE works incrementally, it has potential for being used in online processing. In our experiments, we visualise the advantages of ACE in varying experimental scenarios (except for one special case) and in a state-of-the-art dataset which has been generated for neuro-scientific research under most realistic conditions.