Convergence Properties of Three Spike-Triggered Analysis Techniques
Published in:
Network: Computation in Neural Systems, 14:437-464, 2003
© Institute of Physics Publishing
We analyse the convergence properties of three spike-triggered data
analysis techniques. Our results are obtained in the setting of a
probabilistic linear-nonlinear (LN) cascade neural model; this model
has recently become popular in the study of the neural coding of
natural signals. We start by giving exact rate-of-convergence results
for the common spike-triggered average technique. Next, we analyse a
spike-triggered covariance method, variants of which have been
recently exploited successfully by Bialek, Simoncelli and
colleagues. Unfortunately, the conditions that guarantee that these
two estimators will converge to the correct parameters are typically
not satisfied by natural signal data. Therefore, we introduce an
estimator for the LN model parameters which is designed to converge
under general conditions to the correct model. We derive the rate of
convergence of this estimator, provide an algorithm for its
computation and demonstrate its application to simulated data as well
as physiological data from the primary motor cortex of awake behaving
monkeys. We also give lower bounds on the convergence rate of any
possible LN estimator. Our results should prove useful in the study of
the neural coding of high-dimensional natural signals.
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