Efficient spline regression for neural spiking data.

Mehrad Sarmashghi,Uri Eden,Shantanu P Jadhav,Daniele Avitabile

doi:10.1371/journal.pone.0258321

Mehrad Sarmashghi, Uri Eden + Show 2 more

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https://doi.org/10.1371/journal.pone.0258321

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Abstract

Point process generalized linear models (GLMs) provide a powerful tool for characterizing the coding properties of neural populations. Spline basis functions are often used in point process GLMs, when the relationship between the spiking and driving signals are nonlinear, but common choices for the structure of these spline bases often lead to loss of statistical power and numerical instability when the signals that influence spiking are bounded above or below. In particular, history dependent spike train models often suffer these issues at times immediately following a previous spike. This can make inferences related to refractoriness and bursting activity more challenging. Here, we propose a modified set of spline basis functions that assumes a flat derivative at the endpoints and show that this limits the uncertainty and numerical issues associated with cardinal splines. We illustrate the application of this modified basis to the problem of simultaneously estimating the place field and history dependent properties of a set of neurons from the CA1 region of rat hippocampus, and compare it with the other commonly used basis functions. We have made code available in MATLAB to implement spike train regression using these modified basis functions.

Highlights

Statistical neural models are often used to relate the likelihood of observing particular spike patterns in individual neurons to a variety of factors, including biological and behavioral signals, the neuron’s own past spiking history, and the influences of other neurons in a local population [1]
generalized linear models (GLMs) expand upon classic linear models to allow for a broad range of probability models including point process distributions, which are most appropriate for analysing neural spiking
We observe a peak in interspike interval (ISI) between 5-25 ms interval, suggesting that the neuron tends to fire in bursts with short ISIs in its place field

Summary

Introduction

Statistical neural models are often used to relate the likelihood of observing particular spike patterns in individual neurons to a variety of factors, including biological and behavioral signals, the neuron’s own past spiking history, and the influences of other neurons in a local population [1]. Statistical models for neurons in the CA1 region of rat hippocampus have been used to model these neurons’ place field properties, theta rhythmicity and precession [2, 3], and the neuron’s past spiking history [4]. In order to understand neural receptive fields, point process generalized linear models (GLMs) are often used [1, 5,6,7,8]. GLMs expand upon classic linear models to allow for a broad range of probability models including point process distributions, which are most appropriate for analysing neural spiking. GLMs provide robust and computationally efficient methods for estimating model parameters. They provide powerful analysis tools for computing model uncertainty, assessing

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