  In this paper we consider the problem of detecting statistically significant
sequential patterns in multi-neuronal spike trains. These patterns are
characterized by ordered sequences of spikes from different neurons with
specific delays between spikes. We have previously proposed a data mining
scheme to efficiently discover such patterns which are frequent in the sense
that the count of non-overlapping occurrences of the pattern in the data stream
is above a threshold. Here we propose a method to determine the statistical
significance of these repeating patterns and to set the thresholds
automatically. The novelty of our approach is that we use a compound null
hypothesis that includes not only models of independent neurons but also models
where neurons have weak dependencies. The strength of interaction among the
neurons is represented in terms of certain pair-wise conditional probabilities.
We specify our null hypothesis by putting an upper bound on all such
conditional probabilities. We construct a probabilistic model that captures the
counting process and use this to calculate the mean and variance of the count
for any pattern. Using this we derive a test of significance for rejecting such
a null hypothesis. This also allows us to rank-order different significant
patterns. We illustrate the effectiveness of our approach using spike trains
generated from a non-homogeneous Poisson model with embedded dependencies.
