Abstract
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.
Highlights
It has long been suggested that fundamental insight into the nature of neuronal computation requires the understanding of the cooperative dynamics of populations of neurons (Hebb, 1949)
We have recently presented a novel method for a cumulant-based inference for the presence of higher-order correlations (CuBIC) that avoids the need for extensive sample sizes (Staude et al, 2007, 2009)
The adapted cumulant-based inference of higher-order correlations (CuBIC) As opposed to Section “Stimulus-driven Non-stationarity” where properties of the carrier rate could be inferred from the stimulus, we here cannot make qualitative guesses about the type of nonstationarity
Summary
It has long been suggested that fundamental insight into the nature of neuronal computation requires the understanding of the cooperative dynamics of populations of neurons (Hebb, 1949). Has been substituted with the solution of Eq with objective function Eq and additional constraint β2 ≤ 1/2, and (b) Var[k3] was computed with the algorithm explained in Section “Variance of Test Statistic” with the cumulants of the rate variable R given in Section “Cumulants of Carrier Distributions ” in Appendix.
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