Low-dimensional models of neural population activity in sensory cortical circuits

Neural responses in visual cortex are influenced by visual stimuli and by ongoing spiking activity in local circuits. An important challenge in computational neuroscience is to develop models that can account for both of these features in large multi-neuron recordings and to reveal how stimulus representations interact with and depend on cortical dynamics. Here we introduce a statistical model of neural population activity that integrates a nonlinear receptive field model with a latent dynamical model of ongoing cortical activity. This model captures temporal dynamics and correlations due to shared stimulus drive as well as common noise. Moreover, because the nonlinear stimulus inputs are mixed by the ongoing dynamics, the model can account for a multiple idiosyncratic receptive field shapes with a small number of nonlinear inputs to a low-dimensional dynamical model. We introduce a fast estimation method using online expectation maximization with Laplace approximations, for which inference scales linearly in both population size and recording duration. We test this model to multi-channel recordings from primary visual cortex and show that it accounts for neural tuning properties as well as cross-neural correlations.