Additive Continuous-time Joint Partitioning of Neural Variability

Abstract

Accurate estimation of neural spike-rates is challenging due to fact that both stimulus-dependent spikerates and trial-by-trial noise are continuously timevarying and that neural spiking is well known to exhibit super-or sub-Poisson behavior. In particular, the time-varying nature of the noise makes spikecount statistics sensitive to choices in temporal binsize selection (Cohen & Kohn, 2011). While methods have been proposed for both binless rate estimation and non-Poisson activity (R. Goris, Movshon, & Simoncelli, 2014; Charles, Park, Weller, Horwitz, & Pillow, 2018), no current over-dispersion model can perform arbitrary continuous-time rate estimation. We present here such a model, where we model the stimulus-based rate as a Gaussian Process (GP), and the rate driving the observed spiking is an additive combination of the stimulus GP and a noise process (also modeled as a GP), passed through a rectifying nonlinearity. Our model significantly generalizes previous over-dispersion models by both removing the bin-size dependence, as well as allowing estimation of the latent continuous-time spike-rates. Our model also explains the difference in statistics across bin sizes by accounting for temporal correlations. Given the noise parameters, we can estimate the stimulus GP via a maximum a-posteriori optimization, using a Laplace approximation to marginalize over the noise instantiations. We demonstrate out model both on simulated data as well as macaque V1 activity.

How distinct sources of nuisance variability in natural images and scenes limit human stereopsis

“…But neurophysiological methods would be required to identify and partition sources of noise internal to the nervous system that may arise at various stages of the visual processing and perceptual decision making pipeline. Paradigms that blend the advantages of the current approach for partitioning stimulus-based variation with neurophysiological and computational methods for partitioning noise would be a useful way forward (Ziemba et al, 2016; Goris et al, 2014; Charles & Pillow, 2018).…”