Partitioning Neural Co-Variability

Individual sensory neurons signal precise stimulus information despite high trial-to-trial variability.. Much of this variability is overdispersed — spike-count variance exceeds the mean — and can be partitioned into a stimulus-driven component and a gain that fluctuates across repeated presentations of the same stimulus. While the structure of neural activity, i.e., the stimulus-driven portion of the spike rate, has been explored widely in modeling population-level activity, the role of how modulatory gain factors are shared between neurons or changes over time has not been as thoroughly explored. Recovering the latent structure of the gains would offer a way to separate the stimulus drive from the shared gain that modulates a population over time. Most current overdispersion models thus treat each neuron's gain as independent across neurons and time. To capture the network-level statistics of the population, we thus present the Poisson matrix-normal latent variable model (PMNLV), which extends single-neuron overdispersion to neural populations and across trials, allowing the stimulus drive and the shared population gain to be estimated jointly rather than assumed independent. The model places a matrix-normal prior on the latent gain, and binned spike counts are drawn as Poisson from a rate that sums a per-neuron tuning term and the latent gain passed through a soft-rectifying link; its only structural assumption is a Kronecker factorization of the gain covariance into a neuron factor and a time factor. We derive a variational expectation-maximization algorithm that recovers both factors together with the tuning curves. On synthetic data the algorithm recovers the tuning curves and the covariance factors, and remains accurate at firing rates as low as 0.3 Hz. Compared against related population and overdispersion methods, PMNLV compares favorably in recovering the underlying covariance structure. Applied to Neuropixels recordings from mouse visual cortex, we find that the population's activity covariance and its estimated gain covariance are spectrally misaligned, indicating that the drivers of gain covariance may operate separately from the activity covariance. The PMNLV framework applies to any simultaneously recorded population in which structured gain covariance is of scientific interest, providing a tool for basic neuroscience that resolves population-level structure without compromising single-neuron statistics.