TY - JOUR
T1 - Dethroning the Fano factor
T2 - A flexible, model-based approach to partitioning neural variability
AU - Charles, Adam S.
AU - Park, Mijung
AU - Weller, J. Patrick
AU - Horwitz, Gregory D.
AU - Pillow, Jonathan William
N1 - Funding Information:
We are grateful to Arnulf Graf and J. Anthony Movshon for V1 spike count data used for fitting and validating the flexible overdispersion model. A.S.C. was supported by the NIH NRSA Training Grant in Quantitative Neuroscience (T32MH065214). M.P. was supported by the Gatsby Charitable Foundation. J.W.P. and G.H. were supported by NIH grant EY018849. J.W.P. was supported by grants from the McKnight Foundation, Simons Collaboration on the Global Brain (SCGB AWD1004351), the NSF CAREER Award (IIS-1150186), and an NIMH grant (MH099611)
Publisher Copyright:
© 2018 Massachusetts Institute of Technology.
PY - 2018/4/1
Y1 - 2018/4/1
N2 - Neurons in many brain areas exhibit high trial-to-trial variability, with spike counts that are overdispersed relative to a Poisson distribution. Recent work (Goris, Movshon, & Simoncelli, 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 sublinear to linear to quadratic. Intriguingly, a rectified squaring nonlinearity produces a linear mean-variance function, corresponding to responses with a 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 a nonquadratic relationship between mean and variance. Finally, we demonstrate a practical use of our model via 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.
AB - Neurons in many brain areas exhibit high trial-to-trial variability, with spike counts that are overdispersed relative to a Poisson distribution. Recent work (Goris, Movshon, & Simoncelli, 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 sublinear to linear to quadratic. Intriguingly, a rectified squaring nonlinearity produces a linear mean-variance function, corresponding to responses with a 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 a nonquadratic relationship between mean and variance. Finally, we demonstrate a practical use of our model via 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.
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U2 - 10.1162/NECO_a_01062
DO - 10.1162/NECO_a_01062
M3 - Letter
C2 - 29381442
AN - SCOPUS:85044255891
SN - 0899-7667
VL - 30
SP - 1012
EP - 1045
JO - Neural computation
JF - Neural computation
IS - 4
ER -