Abstract:
|
Thanks to advances in imaging technology and genetic engineering, it is now possible to record neural spiking activity at cellular resolution on live subjects. Such data offer opportunities for deeper understanding of how the brain works, but, on the other hand, they are often challenging to analyse: A typical recording consists of spike times of hundreds or thousands of neurons during a very limited time period, while the observed neuronal activity is temporally dependent with an unknown dependence structure. In this talk, we consider the task of modelling large-scale neural ensembles using the multivariate Hawkes process. The Hawkes process is a point process where a past event might affect the occurrence of future events. We propose an efficient procedure for estimating the sparse graphical structure encoded in the Hawkes process. We demonstrate the use of this procedure on both synthetic data and real data. Finally, we extend the existing theory on Hawkes process to allow for non-excitatory relationships, and show that the proposed procedure recovers the true graph with high probability.
|