# Inferring effective networks of spiking neurons using a continuous-time estimator of transfer entropy

## TL;DR

This paper introduces a new method for inferring effective networks from spike train data using a continuous-time estimator of transfer entropy.

## Contribution

The paper demonstrates the first successful use of a continuous-time TE estimator for inferring effective networks from spike trains.

## Key findings

- The continuous-time TE estimator outperforms pairwise TE and convolutional neural network approaches in inferring effective networks.
- The method performs better than Generalised Linear Models in cases of high synchrony in spike trains.
- The approach reveals how effective connections develop in recordings of developing neural cell cultures.

## Abstract

When analysing high-dimensional time-series datasets, the inference of effective networks has proven to be a valuable modelling technique. This technique produces networks where each target node is associated with a set of source nodes that are capable of providing explanatory power for its dynamics. Multivariate Transfer Entropy (TE) has proven to be a popular and effective tool for inferring these networks. Recently, a continuous-time estimator of TE for event-based data such as spike trains has been developed which, in more efficiently representing event data in terms of inter-event intervals, is significantly more capable of measuring multivariate interactions. The new estimator thus presents an opportunity to more effectively use TE for the inference of effective networks from spike trains, and we demonstrate in this paper for the first time its efficacy at this task. Using data generated from models of spiking neurons—for which the ground-truth connectivity is known—we demonstrate the accuracy of this approach in various dynamical regimes. We further show that it exhibits far superior inference performance to a pairwise TE-based approach as well as a recently-proposed convolutional neural network approach. Moreover, comparison with Generalised Linear Models (GLMs), which are commonly applied to spike-train data, showed clear benefits, particularly in cases of high synchrony. Finally, we demonstrate its utility in revealing the patterns by which effective connections develop from recordings of developing neural cell cultures.

Network inference is a useful technique for the analysis of high-dimensional time series. It allows us to reduce the complexity of the raw data to a network summarising the relationships between the different elements of the time series. Effective networks in neuroscience perform this task by finding the smallest set of source elements which provide maximum explanatory power for the activity of each target node. A directed connection is then drawn from each parent to each target. Transfer Entropy (TE) is a popular tool for inferring these networks. However, the use of TE to infer effective networks from spike train data had previously been limited by the lack of a good estimator of TE for this class of data. This paper demonstrates that a recently-proposed continuous-time estimator of TE on spike trains, when combined with an existing greedy algorithm, is a powerful tool for inferring effective networks.