Liam Paninski, 10/21/03
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Maximum likelihood estimation of cascade point-process neural
encoding models
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Recent work has examined the estimation of models of stimulus-driven
neural activity in which some linear filtering process is followed by
a nonlinear, probabilistic spiking stage.  We analyze the estimation
of one such model for which this nonlinear step is implemented by a
known parametric function.  The assumption that this function is known
can speed up the estimation process considerably, albeit at the cost
of significantly less generality.  We investigate the shape of the
likelihood function for this model, give a simple condition on the
nonlinearity ensuring that no local maxima exist in the likelihood
(leading, in turn, to an efficient algorithm for the computation of
the maximum likelihood estimator), and discuss some of the
implications of this condition for the form of the allowed
nonlinearities.