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

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Maximum likelihood estimation of a stochastic integrate-and-fire neural encoding model (2004)

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by Liam Paninski , Jonathan W. Pillow , Eero P. Simoncelli

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@MISC{Paninski04maximumlikelihood,
    author = {Liam Paninski and Jonathan W. Pillow and Eero P. Simoncelli},
    title = {Maximum likelihood estimation of a stochastic integrate-and-fire neural encoding model},
    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.

Keyphrases

maximum likelihood estimation stochastic integrate-and-fire neural model unique global maximum numerical simulation extracellular spike train response integrate-and-fire spike generation mechanism neural response realistic alternative maximum likelihood estimator model validity density evolution technique spike generation linear filtering stage maximum likelihood solution efficient algorithm log likelihood function model parameter intracellular voltage data gradient ascent technique

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