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Analyzing Short-Term Noise Dependencies of Spike-Counts in Macaque Prefrontal Cortex Using Copulas and the Flashlight Transformation
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@MISC{Onken_analyzingshort-term,
author = {Arno Onken and Steffen Grünewälder and Matthias H. J. Munk and Klaus Obermayer},
title = {Analyzing Short-Term Noise Dependencies of Spike-Counts in Macaque Prefrontal Cortex Using Copulas and the Flashlight Transformation},
year = {}
}
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Abstract
Simultaneous spike-counts of neural populations are typically modeled by a Gaussian distribution. On short time scales, however, this distribution is too restrictive to describe and analyze multivariate distributions of discrete spike-counts. We present an alternative that is based on copulas and can account for arbitrary marginal distributions, including Poisson and negative binomial distributions as well as second and higher-order interactions. We describe maximum likelihood-based procedures for fitting copula-based models to spike-count data, and we derive a so-called flashlight transformation which makes it possible to move the tail dependence of an arbitrary copula into an arbitrary orthant of the multivariate probability distribution. Mixtures of copulas that combine different dependence structures and thereby model different driving processes simultaneously are also introduced. First, we apply copula-based models to populations of integrate-and-fire neurons receiving partially correlated input and show that the best fitting copulas provide information about the functional connectivity of coupled neurons which can be extracted using the flashlight transformation. We then apply the new method to data which were recorded from macaque prefrontal cortex using a multi-tetrode array. We find that copulabased distributions with negative binomial marginals provide an appropriate stochastic model for the multivariate spikecount distributions rather than the multivariate Poisson latent variables distribution and the often used multivariate normal distribution. The dependence structure of these distributions provides evidence for common inhibitory input to all recorded
Keyphrases
flashlight transformation short-term noise dependency macaque prefrontal cortex using copula copula-based model spike-count data short time scale new method functional connectivity macaque prefrontal cortex maximum likelihood-based procedure gaussian distribution multi-tetrode array multivariate spikecount distribution appropriate stochastic model multivariate poisson latent variable distribution arbitrary copula neural population higher-order interaction arbitrary marginal distribution so-called flashlight transformation multivariate probability distribution multivariate distribution discrete spike-counts used multivariate normal distribution arbitrary orthant fitting copula negative binomial distribution tail dependence different dependence structure common inhibitory input negative binomial marginals dependence structure integrate-and-fire neuron simultaneous spike-counts
