How do temporal stimulus correlations influence the performance of
population codes?


It has long been argued that many key questions in neuroscience can
best be posed in information-theoretic terms; the efficient coding
hypothesis discussed by Attneave, Barlow, Atick, et al represents
perhaps the best-known example.  Answering these questions
quantitatively requires us to compute the Shannon information rate of
neural channels, whether numerically using experimental data or
analytically in mathematical models.  The non-linearity and
non-Gaussianity of neural responses has complicated these
calculations, particularly in the case of stimulus distributions with
temporal dynamics and nontrivial correlation structure.

In this work we extend a method proposed in [1] that allows us to
compute the information rate analytically in some cases.  In our
approach the stimulus is modeled as a temporally correlated stationary
process.  Analytical results are available in both the high and low
signal-to-noise (SNR) regimes: the former corresponds to the case in
which a large population of neurons responds strongly to the stimulus,
while the latter implies that the available neurons are only weakly
tuned to the stimulus properties, or equivalently that the stimulus
magnitude is relatively small.  In intermediate SNR regimes, good
numerical approximations to the information rate are available using
efficient forward-backward decoding methods and Laplace approximations
[2,3].

We find that when the number of neurons increases unboundedly, the
mutual information for temporarily correlated stimuli has a simple
form depending only on the Fisher information, paralleling the
classical connection between Fisher and Shannon information for static
stimuli [4].  For finite-size populations we are able to calculate the
performance difference between a decoder based solely on temporally
instantaneous observations and one which integrates temporal
observations; interestingly, in both the high- and low-SNR regimes, a
simple decoder which only includes temporally local neural responses
is able to optimally extract information about the stimuli.


References:

[1] Barbieri, R. et al. (2004). Dynamic analyses of information
encoding in neural ensembles.  Neural Computation.

[2] Paninski et al. (2009).  A new look at state-space models for
neural data.  J. Comput. Neurosci.

[3] Pillow et al. (2009).  Model-based decoding, information
estimation, and change-point detection in multi-neuron spike trains.
Under review.

[4] Brunel, N. and Nadal, J.-P. (1998). Mutual information, Fisher
information, and population coding.  Neural Computation.