Inferring synaptic interactions and transmission delays

We proposed a mapping of the spiking activity to high-dimensional spaces, termed event spaces, spanned by the inter-spike intervals of a selected neuron and the respective cross-spike intervals of the rest of the network. The mapping from the raster plot to the event spaces may be viewed as a sampling of the inter-spike interval generating function for each neuron. To identify the effect of putative pre-synaptic neurons to a post-synaptic one we proposed a geometric approximation of the inter-spike interval generating function around a reference point (reference event). To identify the transmission delays, we proposed the minimisation of the approximation error in the space of interaction delays. To speed up the optimisation and avoid local minima, we optimised the delays on a smoothed error landscape approximated by radial basis function interpolation.

Here is an extension of the method that I wrote up as a mini-project in parallel with my thesis that improves the reconstruction performance in settings with irregular spiking activity. The clue in this case is to look at the singular components with less variability (minor components) because they represent the directions in the event space with consistent firing patterns that correspond to causal interactions between neurons, while the dominant/principal component capture the variability of the irregular activity. See evidence in Figure 2 in the report. This didn’t make it in the final paper, but I’ve always found it a neat feat.

Resulted in the paper Casadiego*, Maoutsa*, Timme; Physical Review Letters 2018