Maximum Likelihood Estimation of a Stochastic Integrate-and-Fire Neural Encoding Model

Authors:
Liam Paninski;Jonathan W. Pillow;Eero P. Simoncelli
Affiliations:
Howard Hughes Medical Institute, Center for Neural Science, New York University, New York, NY 10003, U.S.A., and Gatsby Computational Neuroscience Unit, University College London, London WC1N 3AR, ...;Howard Hughes Medical Institute, Center for Neural Science, New York University, New York, NY 10003, U.S.A.;Howard Hughes Medical Institute, Center for Neural Science, and Courant Institute for Mathematical Science, New York University, New York, NY 10003, U.S.A.
Venue:
Neural Computation
Year:
2004

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Abstract

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 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.