Maximum likelihood estimation of a stochastic integrate-and-fire cascade spiking model

L M Paninski, J W Pillow and E P Simoncelli

Published in Annual Meeting, Neuroscience, Nov 2003.

This paper has been superseded by:
Maximum likelihood estimation of a stochastic integrate-and-fire neural encoding model
L Paninski, J Pillow and E P Simoncelli.
Neural Computation, vol.16(12), pp. 2533--2561, Dec 2004.

A variety of models of stimulus-driven neural activity are of cascade form, in which a linear filter is followed by a nonlinear probabilistic spiking mechanism. One simple version of this model implements the nonlinear stage as a noisy, leaky, integrate-and-fire mechanism. This model is a more biophysically realistic alternative to models with Poisson (memory-less) spiking, and has been shown to be effective in reproducing various spiking statistics of neurons in vivo. However, the estimation of the full model parameters from extracellular spike train data has not been examined in depth.

We address this problem here in two steps. First, we show how the problem can be formulated in terms of maximum likelihood estimation, which provides a statistical setting and natural 'cost function' for the problem. Second, we show that the computational problem of optimizing this cost function is tractable: we provide a proof that the likelihood function has a single global optimimum and introduce an algorithm that is guaranteed to find this optimum with reasonable efficiency. We demonstrate the effectiveness of our estimator with numerical simulations and apply the model to both in vitro and in vivo data.


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  • CNS*02 article: Pilow02a
  • Book chapter on neural characterization: Simoncelli03c
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