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

Liam Paninski, Jonathan Pillow, and Eero Simoncelli

Neural Computation 16: 2533-2561 (2004).

We examine a cascade encoding model for neural response in which a linear filtering stage is followed by a noisy, leaky, integrate-and-fire spike generation mechanism. This model provides a biophysically more realistic alternative to models based on Poisson (memoryless) spike generation, and can effectively reproduce a variety of spiking behaviors seen {\it in vivo}. We describe the maximum likelihood estimator for the model parameters, given only extracellular spike train responses (not intracellular voltage data). Specifically, we prove that the log likelihood function is concave and thus has an essentially unique global maximum that can be found using gradient ascent techniques. We develop an efficient algorithm for computing the maximum likelihood solution, demonstrate the effectiveness of the resulting estimator with numerical simulations, and discuss a method of testing the model's validity using time-rescaling and density evolution techniques.

**Note: we recently re-examined the proof of theorem 1 in the paper, and we have found a questionable step. The statement of log-concavity in all variables except for the membrane conductance g remains unchanged (ie, the likelihood is unimodal in all the other variables if g is held fixed); however, we are no longer sure whether the statement about unimodality in g holds. We'll publish an update once the situation is more clear.
Reprint (600K, pdf)  |  Liam Paninski's research page
Related work on likelihood-based estimation of neural models|  on the integrate-and-fire cell

*A short version of this work appeared in the NIPS 2003 proceedings.