Maximum likelihood estimation of a stochastic integrate-and-fire neural encoding model

Jonathan W. Pillow, Liam Paninski and Eero P. Simoncelli
 
Advances in Neural Information Processing Systems, eds S. Thrun, L. Saul and B. Schölkopf, vol 16, May 2004, MIT Press, Cambridge MA. (2004)

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 noisy, leaky, integrate-and-fire mechanism with a spike-dependent aftercurrent. This model is a biophysically plausible alternative to models with Poisson (memory-less) spiking, and has been shown to effectively reproduce various spiking statistics of neurons in vivo. However, the problem of estimating the model from extracellular spike train data has not been examined in depth. We formulate the problem in terms of maximum likelihood estimation, and show that the computational problem of maximizing the likelihood is tractable. Our main contribution is an algorithm and a proof that this algorithm is guaranteed to find the global optimum with reasonable speed. We demonstrate the effectiveness of our estimator with numerical simulations.

 
related:
  • this paper is superceded by: paninski-NC-04
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