Flexible models for spike count data with both over- and under- dispersion

Stevenson, I. H.

doi:10.1007/s10827-016-0603-y

Cited by 31 publications

(47 citation statements)

References 77 publications

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“…This framework includes the multiplicative Goris model as a special case when the nonlinearity is exponential, but includes the flexibility to exhibit other behaviors as well: for example, Fano factors that decrease with increasing spike rate, which arises for a rectified-linear nonlinearity, and constant slope linear relationships, corresponding to a constant Fano factor, which arises for a rectified squaring nonlinearity. We show that the model can be tractably fit to data using the Laplace approximation to compute likelihoods, and requires fewer parameters than other models for non-Poisson spike count data such as the modulated binomial or generalized count models (Gao et al, 2015;Stevenson, 2016). We apply our model to the V1 dataset presented in Goris et al (2014) and show that a rectified power-law nonlinearity provides a better description of most individual neurons than a purely multiplicative model.…”

Section: Introductionmentioning

confidence: 90%

“…This model makes the strong assumption that the mean and variance are equal: var[r] = E[r] = λ(x), for any stimulus x. A sizeable literature has shown assumption is often inaccurate, as spike counts in many brain areas exhibit over-dispersion relative to the Poisson distribution, meaning that variance exceeds the mean (Shadlen & Newsome, 1998;Gur et al, 1997;Barberini et al, 2001;Pillow & Scott, 2012b;Gao et al, 2015;Goris et al, 2014;Stevenson, 2016;Baddeley et al, 1997;Gershon et al, 1998;Tolhurst et al, 1983;Buracas et al, 1998;Carandini, 2004).…”

Section: Background: Fano Factor and The Modulated Poisson Modelmentioning

confidence: 99%

“…A substantial literature has shown that Fano factors in a variety of different brain areas differ substantially from 1 (Shadlen & Newsome, 1998;Gur et al, 1997;Barberini et al, 2001;Baddeley et al, 1997;Gershon et al, 1998). Recent work has shown that, not only do neural responses not obey a Poisson distribution, the overall mean-variance relationship is often not well characterized by a line, meaning the data are not consistent with a single Fano factor (Pillow & Scott, 2012b;Gao et al, 2015;Stevenson, 2016;Goris et al, 2014;Wiener & Richmond, 2003;Moshitch & Nelken, 2014). Rather, the spike count variance changes nonlinearly with mean.…”

Section: Introductionmentioning

confidence: 99%

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

Charles

Park

Weller

et al. 2017

Preprint

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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.

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Section: Introductionmentioning

confidence: 90%

Section: Background: Fano Factor and The Modulated Poisson Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Charles

Park

Weller

et al. 2017

Preprint

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“…On each trial, we analyzed 96 spike counts during the window 150 ms before to 350 ms after the speed reached its half-max. Detailed 97 descriptions of the surgical procedure, behavioral task, and preprocessing are available in the original 98 report (Stevenson, 2016). 99…”

Section: Neural Data 88mentioning

confidence: 99%

“…In previous work we described how CMP models can provide more accurate descriptions of trial-to-trial 148 variability for tuning curves (Stevenson, 2016). The CMP distribution takes the form: 149 In practice, we take advantage of the fact that the CMP distribution is in the exponential family and 156 frame the problem of tuning curve estimation as a generalized linear model (GLM) (Sellers et al, 2012).…”

Section: Conway-maxwell-poisson Models 147mentioning

confidence: 99%

Modeling stimulus-dependent variability improves decoding of population neural responses

Ghanbari

Christopher

Read

et al. 2017

Preprint

Self Cite

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Neural responses to repeated presentations of an identical stimulus often show substantial trial-totrial variability. Although the mean firing rate in response to different stimuli or during different movements (tuning curves) have been extensively modeled, the variability of neural responses can also have clear tuning independent of the tuning in the firing rate. This suggests that the variability carries information regarding the stimulus/movement beyond what is encoded in the mean firing rate. Here we demonstrate how taking variability into account can improve neural decoding.In a typical neural coding model spike counts are assumed to be Poisson with the mean response depending on an external variable, such as a stimulus/movement direction. Bayesian decoding methods then use the probabilities under these Poisson tuning models (the likelihood) to estimate the probability of each stimulus given the spikes on a given trial (the posterior). However, under the Poisson model, spike count variability is always exactly equal to the mean (Fano Factor = 1). Here we use the Conway-Maxwell-Poisson (COM-Poisson) model to more flexibly model how neural variability depends on external stimuli. This model contains the Poisson distribution as a special case, but has an additional parameter that allows both over-and underdispersed data, where the variance is greater than (Fano Factor >1) or less than (Fano Factor <1) the mean, respectively.We find that neural responses in both primary motor cortex (M1) and primary visual cortex (V1) have diverse tuning in both their mean firing rates and response variability. These tuning patterns can be accurately described by the COM-Poisson model, and, in both cortical areas, we find that a Bayesian decoder using the COM-Poisson models improves stimulus/movement estimation by 4-8% compared to the Poisson model. The additional layer of information in response variability thus appears to be an important part of the neural code. .For spike counts the distribution is a function of the intensity and dispersion parameters and with < 1 describing over-dispersion and > 1 describing under-dispersed data. Note that with = 1 the COM-Poisson is exactly the Poisson distribution. Here we use the COM-Poisson distribution as the noise model for a GLM [1] to estimate both the mean and variance of neural responses to varying stimuli/movement. In particular, we estimate parameters and γ that map stimulus/movement covariates ( ) and ( ) to neural responses using the link functions log ( ) = ( ) and log( ( )) = ( ) . This framework is in effect a dual-link GLM where both the mean and the variance depend on the stimulus/movement direction θ.Here we estimate the tuning curves using spline bases and maximum a posteriori (MAP) estimation with L2 regularization. Importantly, this approach allows us to model neural responses that are under-dispersed, overdispersed, or that contain intermingled under-and over-dispersed counts [2]. Using the tuning curve models to describe the likelihood of spike responses, ...

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Latent Variable Modeling of Neural Population Dynamics

Chen

2018

Dynamic Neuroscience

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Flexible models for spike count data with both over- and under- dispersion

Cited by 31 publications

References 77 publications

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

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

Modeling stimulus-dependent variability improves decoding of population neural responses

Latent Variable Modeling of Neural Population Dynamics

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