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Benjamin Staude

The cell assembly hypothesis [1] postulates dynamically interacting groups of neurons as building blocks of cortical information processing. Synchronized spiking across large neuronal groups was later suggested as a potential signature for active assemblies [2], predicting higher-order correlations (HOCs) among the spike trains of assembly members. However, the estimation of the necessary parameters of present analysis techniques for HOCs poses serious problems, mainly because their number grows exponentially with the number of recorded neurons [3,4]. As a consequence, most attempts to detect active cell assemblies resort to pairwise correlations. Such pairwise correlations, however, do not reflect potential HOCs and are insensitive for sparse synchronous events [5]. As massively parallel extracellular recordings are becoming more and more available, the limited experimental evidence in favor of the cell assembly hypothesis has to a large extent be assigned to a lack of suitable analysis tools [6].

Here we present a novel procedure to detect HOCs in massively parallel
spike trains. Based on estimates of only a few low-order cumulants of
the summed activity across all neurons (the 'population histogram') we
devise a statistical test for the presence of HOCs among the recorded
spike trains. The test exploits the fact that absence of HOCs in a
neuronal population also imposes constraints on (population-average)
correlations of lower order. The latter can, however, be estimated via
the respective cumulants of the the distribution of the entries in the
population histogram. Under a compound Poisson assumption, where
correlations of various orders are induced by 'inserting' appropriate
patterns of near-synchronous spikes [7], the upper bounds for these
lower order cumulants in the absence of HOCs can be derived
analytically, together with the necessary confidence intervals of the
respective k-statistics. This makes the test computationaly very
modest and hence applicable to large amounts of data without the need
for time consuming bootstrap approaches. Furthermore, the inference of
HOCs from cumulants of lower order circumvents the need to estimate
large numbers of higher-order parameters, making the test less
susceptible to the limited sample sizes typical for in vivo recordings
than previous approaches [3,4]. We illustrate the test on data which
was simulated using a compound Poisson model, and find that cumulants
of third order are already surprisingly sensitive for present HOCs.
Furthermore, the proposed test detects HOCs even if their effects on
pairwise correlation coefficients *c* are very small (in the
range of *c* ~ 0.01, compare [5]).

[1] D.O. Hebb. Organization of behavior.
Wiley (1949)

[2] M. Abeles. Local cortical circuits.
Springer (1982)

[3] L. Martignon et al. * Biol Cyber.*
**73**:69-81 (1995)

[4] H. Nakahara & S.-I. Amari * Neural Comput.*
**14**:2296-2316 (2002)

[5] E. Schneidman et al. * Nature*
**440**:1007-1012 (2006)

[6] E.N. Brown, R.E. Kass, P.P. Mithra * Nat. Neurosci.*
**7**:456-461 (2004)

[7] A. Kuhn, A. Aertsen and S. Rotter. *Neural Comput.*
**15**:67-101 (2003)