Variational Latent Gaussian Process for Recovering Single-Trial Dynamics from Population Spike Trains

When governed by underlying low-dimensional dynamics, the interdependence of simultaneously recorded population of neurons can be explained by a small number of shared factors, or a low-dimensional trajectory. Recovering these latent trajectories, particularly from single-trial population recordings, may help us understand the dynamics that drive neural computation. However, due to the biophysical constraints and noise in the spike trains, inferring trajectories from data is a challenging statistical problem in general. Here, we propose a practical and efficient inference method, called the variational latent Gaussian process (vLGP). The vLGP combines a generative model with a history-dependent point process observation together with a smoothness prior on the latent trajectories. The vLGP improves upon earlier methods for recovering latent trajectories, which assume either observation models inappropriate for point processes or linear dynamics. We compare and validate vLGP on both simulated datasets and population recordings from the primary visual cortex. In the V1 dataset, we find that vLGP achieves substantially higher performance than previous methods for predicting omitted spike trains, as well as capturing both the toroidal topology of visual stimuli space, and the noise-correlation. These results show that vLGP is a robust method with a potential to reveal hidden neural dynamics from large-scale neural recordings.