Modeling stimulus-dependent variability improves decoding of population neural responses

Abstract

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, ...