Neuronal connectivity inference from spike trains using an empirical probabilistic causality measure

Abstract

To fully understand the computational properties of aneural network, it is crucial to know the network's connec-tivity. Unfortunately, connectivity inference using easilyaccessible data such as extracellular spike recordings is adifficult task. The difficulty arises mainly from problemsrelated with causality, polysynaptic (indirect) connectiv-ity, inhibition and variable time delays, just to name afew. Different methods have been proposed for connectiv-ity inference using, for example, mutual information[1,2], partial directed coherence [3], direct neuronaldynamics parameters fitting [4] or parameter estimationusing Bayesian approaches [5]. However, we argue thatmost of these methods are too complex to implement,hard to apply to spike times series or simply do not pro-vide appropriate estimations using benchmark syntheticdata.Here we present an alternative method that takes directlythe series of spike times from multiple sources and pro-duces a probabilistic connectivity matrix, wherein eachentry provides a confidence level for the existence of aconnection (excitatory or inhibitory) for a particularsource/target pair. Instead of using measures which aredirectly or indirectly related to correlations, our methodintroduces an empirical measure of causality that workson top of spike time probability distributions obtainedfrom the spike times series. This approach allows us tocope with variable time delays, causality, inhibitory con-nections and provides an estimate for the degree of con-nection (monosynaptic, disynaptic, etc.). Our methodincludes heuristics but only one parameter needs to be set:the causality time window. This value defines the maxi-mum time delay between two events that are said to berelated and is used to constrain the causality search space.Our method has been tested using synthetic data fromsimulations where the neuronal connectivity is known