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Abstract

Population activity in primary visual cortex exhibits substantial variability that is correlated on multiple time scales and across neurons [1]. A quantitative account of how
visual information is encoded in population of neurons in primary visual cortex therefore requires an accurate characterization of this variability. Our goal is provide a statistical model for capturing the statistical structure of this variability and its dependence on external stimuli, with particular focus on temporal correlations both on short (withintrial) and long (across-trial) time-scales [2]. We address this question using neural population recordings from primary visual cortex in response to drifting gratings [3], using the framework of generalized linear models (GLMs). To model stimulus-driven responses, we take a non-parametric approach and employ Gaussian-process priors to model the smoothness of response-profiles across time and different stimulus orientations, and low-rank constraints to facilitate inference from limited data. We find that the parameters which control the prior smoothness are consistent across neurons within each recording session, but differ markedly across recordings. For most neurons, the time-varying response across all stimulus orientations can be well captured using a lowrank
decomposition with k = 4 dimensions. To capture slow modulations in firing rates, we include covariates in the GLM which are constrained to vary smoothly across trials,
and find that including these terms leads to significant improvements in goodness-of-fit. Finally, we use latent dynamical systems [3] with point-process observation models [4] to capture variations and co-variations in firing rates on fast time-scales. While we focus our analysis on modelling neural population responses in V1, our approach provides a general formalism for obtaining an accurate quantitative model of response variability in neural populations.