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Abstract:
We present an information-geometric measure to systematically
investigate neuronal firing patterns, taking account not only of
the second-order but also of higher-order interactions. We begin
with the case of two neurons for illustration and show how to
test whether or not any pairwise correlation in one period is
significantly different from that in the other period. In order
to test such a hypothesis of different firing rates, the
correlation term needs to be singled out `orthogonally' to the
firing rates, where the null hypothesis might not be of
independent firing. This method is also shown to directly
associate neural firing with behavior via their mutual
information, which is decomposed into two types of information,
conveyed by mean firing rate and coincident firing, respectively.
Then, we show that these results, using the `orthogonal'
decomposition, are naturally extended to the case of three
neurons and n neurons in general.
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