Recurrent linear models of simultaneously-recorded neural populations

Population neural recordings with long-range temporal structure are often best understood in terms of a common underlying low-dimensional dynamical process. Advances in recording technology provide access to an ever-larger fraction of the population, but the standard computational approaches available to identify the collective dynamics scale poorly with the size of the dataset. We describe a new, scalable approach to discovering low-dimensional dynamics that underlie simultaneously recorded spike trains from a neural population. We formulate the Recurrent Linear Model (RLM) by generalising the Kalman-filter-based likelihood calculation for latent linear dynamical systems to incorporate a generalised-linear observation process. We show that RLMs describe motor-cortical population data better than either directly-coupled generalised-linear models or latent linear dynamical system models with generalised-linear observations. We also introduce the cascaded generalised-linear model (CGLM) to capture low-dimensional instantaneous correlations in neural populations. The CGLM describes the cortical recordings better than either Ising or Gaussian models and, like the RLM, can be fit exactly and quickly. The CGLM can also be seen as a generalisation of a low-rank Gaussian model, in this case factor analysis. The computational tractability of the RLM and CGLM allow both to scale to very high-dimensional neural data.