## Maximum likelihood estimation of cascade point-process
neural encoding models

Network: Computation
in Neural Systems 15: 243-262.

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
speeds the estimation process considerably. We investigate the shape
of the likelihood function for this type of model, give a simple
condition on the nonlinearity ensuring that no non-global local maxima
exist in the likelihood --- leading, in turn, to efficient algorithms
for the computation of the maximum likelihood estimator --- and
discuss the implications for the form of the allowed nonlinearities.
Finally, we note some interesting connections between the
likelihood-based estimators and the classical spike-triggered average
estimator, discuss some useful extensions of the basic model
structure, and provide two novel applications to physiological data.

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Paninski's research