Higher-order correlations in non-stationary parallel spike trains: statistical modeling and inference.

The extent to which groups of neurons exhibit higher-order correlations in their spiking activity is a controversial issue in current brain research. A major difficulty is that currently available tools for the analysis of massively parallel spike trains (N >10) for higher-order correlations typically require vast sample sizes. While multiple single-cell recordings become increasingly available, experimental approaches to investigate the role of higher-order correlations suffer from the limitations of available analysis techniques. We have recently presented a novel method for cumulant-based inference of higher-order correlations (CuBIC) that detects correlations of higher order even from relatively short data stretches of length T = 10-100 s. CuBIC employs the compound Poisson process (CPP) as a statistical model for the population spike counts, and assumes spike trains to be stationary in the analyzed data stretch. In the present study, we describe a non-stationary version of the CPP by decoupling the correlation structure from the spiking intensity of the population. This allows us to adapt CuBIC to time-varying firing rates. Numerical simulations reveal that the adaptation corrects for false positive inference of correlations in data with pure rate co-variation, while allowing for temporal variations of the firing rates has a surprisingly small effect on CuBICs sensitivity for correlations.