Reconstructing the functional connectivity of multiple spike trains using Hawkes models

Statistical models that predict neuron spike occurrence from the earlier spiking activity of the whole recorded network are promising tools to reconstruct functional connectivity graphs. Some of the previously used methods are in the general statistical framework of the multivariate Hawkes processes. However, they usually require a huge amount of data, some prior knowledge about the recorded network, and/or may produce an increasing number of spikes along time during simulation.

Here, we present a method, based on least-square estimators and LASSO penalty criteria, for a particular class of Hawkes processes that can be used for simulation.

Testing our method on small networks modeled with Leaky Integrate and Fire demonstrated that it efficiently detects both excitatory and inhibitory connections. The few errors that occasionally occur with complex networks including common inputs, weak and chained connections, can be discarded based on objective criteria.

With respect to other existing methods, the present one allows to reconstruct functional connectivity of small networks without prior knowledge of their properties or architecture, using an experimentally realistic amount of data.

The present method is robust, stable, and can be used on a personal computer as a routine procedure to infer connectivity graphs and generate simulation models from simultaneous spike train recordings.