Dethroning the Fano Factor: a flexible, model-based approach to partitioning neural variability

Abstract

Neurons in many brain areas exhibit high trial-to-trial variability, with spike counts that are over-dispersed relative to a Poisson distribution. Recent work (Goris et al., 2014) has proposed to explain this variability in terms of a multiplicative interaction between a stochastic gain variable and a stimulus-dependent Poisson firing rate, which produces quadratic relationships between spike count mean and variance. Here we examine this quadratic assumption and propose a more flexible family of models that can account for a more diverse set of mean-variance relationships. Our model contains additive Gaussian noise that is transformed nonlinearly to produce a Poisson spike rate. Different choices of the nonlinear function can give rise to qualitatively different mean-variance relationships, ranging from sub-linear to linear to multiplicative. Intriguingly, a rectified squaring nonlinearity produces a linear mean-variance function, corresponding to responses with constant Fano factor. We describe a computationally efficient method for fitting this model to data, and demonstrate that a majority of neurons in a V1 population are better described by a model with non-quadratic relationship between mean and variance. Lastly, we develop an application to Bayesian adaptive stimulus selection in closed-loop neurophysiology experiments, which shows that accounting for overdispersion can lead to dramatic improvements in adaptive tuning curve estimation.

Relating Divisive Normalization to Neuronal Response Variability

“…Existing normalization models describe only the firing rate, and thus cannot assess the effect of normalization on variability. On the other hand, successful descriptive models of neuronal variability (Paninski, 2004;Pillow et al, 2008;Goris et al, 2014;Charles et al, 2018) typically ignore normalization. We therefore develop a model that explicitly parametrizes this relation and allows us to estimate the relevant parameters from data.…”

Additive Continuous-time Joint Partitioning of Neural Variability

“…R. R. Goris, Ballé, & Simoncelli, 2015;Rabinowitz, Goris, Cohen, & Simoncelli, 2015;Charles et al, 2018). Specifically, our model can be considered a continuous-time extension of previous work on flexible over-dispersion models for binned data (Charles et al, 2018). The extension to continuous time incurs extra complexity in that enough samples of a Gaussian Process need to be estimated to approximate an integral.…”

“…Our model is influenced by recent work in characterizing over-dispersion in neural firing (R. Goris et al, 2014;N. R. R. Goris, Ballé, & Simoncelli, 2015;Rabinowitz, Goris, Cohen, & Simoncelli, 2015;Charles et al, 2018). Specifically, our model can be considered a continuous-time extension of previous work on flexible over-dispersion models for binned data (Charles et al, 2018).…”

“…For the time-bins, both advanced methods to select optimal bin-sizes (Shimazaki & Shinomoto, 2007) or fully continuous time Poisson models that bypass the need to bin at all (Mena & Paninski, 2014;Truccolo, Eden, Fellows, Donoghue, & Brown, 2005) have been proposed. To account for over-and under-dispersion, new models have been proposed to either augment or replace the Poisson model (R. Goris et al, 2014;Charles et al, 2018;Stevenson, 2016;Gao, Busing, Shenoy, & Cunningham, 2015;Pillow & Scott, 2012;Sellers, Borle, & Shmueli, 2012;Moshitch & Nelken, 2014). No method has yet, however, has performed bin-less inference of latent spike-rates under an over-or underdispersed model…”

“…We present here such a model for over-dispersed spike rates. Our method is based on a continuous time extension of previous work that models over-dispersion as latent noise that effects the spike rate through a nonlinearity (Charles et al, 2018). By extending the Poisson perbin count model to a full Poisson process, and extending the latent Gaussian noise to a continuous-time Gaussian Process (GP), we are able to model both of these challenging aspects.…”