Applying non-parametric testing to discrete transfer entropy

Abstract

Transfer entropy (TE) is a powerful algorithm which attempts to detect the transfer of information from one system to another. In neuroscience, it has the potential to track the movement of information through complex neuronal systems, and provide powerful insights into their organization and operation. One such application is the ability to infer the existence of causal connectivity (such as synaptic pathways) between neurons in a culture being recorded by micro-electrode array (MEA).\n\nThere are several challenges, however, in applying TE to neurological data; one of these is the ability to robustly classify what experimental TE value qualifies as significant. We find that common methods in spike train analysis such as a Z-test cannot be applied, as their assumptions are not met. Instead, we utilize surrogate data to compute a sample under the null hypothesis (no causal connection), and resample experimental data through Markov chain Monte Carlo (MCMC) methods to create a sample of TE values under experimental conditions. A standard non-parametric test (Mann-Whitney U-test) is then applied to compare these samples, and determine if they represent a significant connection.\n\nWe have applied this methodology to MEA recordings of neuronal cultures developing over a period of roughly a month, and find that it provides a wealth of information regarding the cultures' maturity. This includes features such as the directed graph of causal connections across the MEA and identification of information exchange centers. These results are consistent and carry a well-defined significance level.