Patricia Reynaud-Bouret - CNRS, LJAD - Keywords: statistics, neuroscience

Patricia Reynaud-Bouret - CNRS, LJAD - Keywords: statistics, neuroscience

Contribution title: Reconstructing the functional connectivity of multiple spike trains using Hawkes models

The difference between functional connectivity and physical connectivity in neuroscience can be understood via a little metaphore. Imagine you want to know what are the main interactions between cities in France. To do that, you could look at a road map: this is the physical connectivity between neurons. But what would be more important to understand the interactions, is to know what are the roads that are used often, in which direction ... and maybe the precise path of the roads is not important, one just want to know if and with whom the cities are communicating and the quality of their communication (say via the number of trucks they are sending in each direction). This is the functional connectivity.
The inference problem of functional connectivity is much more complicated because neuroscientists cannot know where the "trucks" are going, they only know when they are emitted by a city (a "truck" corresponds in fact to an action potential, also called spike, emitted by a neuron). Neuroscientists also know that there might be excitation or inhibition, meaning that when a truck arrive at a given city, it might either increase or decrease the probability for this city to send other trucks.
So the whole problem, translated via this metaphor, is: if one is able to know when each city sends trucks, can we reconstruct the interaction patterns? And this without even looking at the map!
We are using Hawkes processes and Lasso procedures to obtain the answer. We apply it on real data in rat cortical barrels to understand what amount of information on the stimuli is coded in the cortex via the reconstructed functional connectivity graph.