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- A. Onken and
K. Obermayer. Stimulus-Independence of Noise Correlations is Beneficial
for Short-Term Population Coding in MT.
.
In Computational and Systems Neuroscience, @November 2008.
(FTP PDF, 906 kb)
The noise correlation of orientation selective populations in the
middle temporal (MT) area is known to depend on the difference in their
preferred directions [1, 2]. Here, we construct a multivariate Poisson (MVP)
model of spike-counts of an orientation selective population of up to 100 MT
neurons in order to compare the impact of different correlation structures on
coding at a time scale of tens of milliseconds. In accordance with
experimental findings, the model has the following constraints: (1) We assume
von Mises tuning functions with firing rates between 10 Hz and 60 Hz. (2)
Covariances are strictly decreasing for increasing differences in preferred
directions up to a margin with a specified mean of correlation coefficients.
(3) With respect to the number of hidden variables, the model complexity is
minimal subject to the first constraints. We find that a MVP model with only
pairwise correlations cannot reproduce the mean correlations observed
experimentally; on the other hand, the constraints yield a unique higher
order system of correlations. Within this model class, near
stimulus-independence of the correlation coefficients produces the best fit
to the neurophysiological data, i.e. the dependence residue is close to the
experimentally observed one. The model is complemented by a stimulus readout.
We assess the mean square error (MSE) of optimal decoders and compare the
normalized average Kullback-Leibler divergence (ΔI/I) between the
posterior distribution of the true responses and the posterior distribution
of independent responses. Since the computation of the Bayes-optimal
posterior has exponential complexity, we apply an approximation based on an
orthonormal system for the likelihoods. We estimate coding capabilities
within 30 ms windows for different models in the class: one with a
correlation structure that exhibits stimulus-independent covariances and thus
stimulus-dependent correlation coefficients, a model with a structure that
shows near stimulus-independent correlation coefficients (the best fitting
model), and models with intermediate structures. It is found that the best
fitting model is not optimal in terms of the MSE readout performance.
However, ΔI/I turns out to be minimal for the best fitting model.
Furthermore, the readout performance of a MT model without any noise
correlation is better than the readout performance of any model in the
investigated model class. These findings suggest that MT optimizes the
correlation structure in the encoding process to let the resulting posterior
come near to the posterior of a model with independent noise. Therefore, the
findings indicate that MT cannot benefit from noise correlations for
short-term coding.
References:
[1] Correlated firing in macaque
visual area MT: time scales and relationship to behavior. W. Bair, E. Zohary,
and W. T. Newsome, Journal of Neuroscience 21(5):1676-1697, March 2001.
[2] The structure and time course of neuronal correlation in cortical motion
area MT. X. Huang and S. G. Lisberger, Society for Neuroscience Abstracts
33:715.16, November 2007.
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