Maximum likelihood estimation of cascade point-process neural encoding models

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.