Estimating a Separable Random Field from Binary Observations

Stochastic processes with dynamics at multiple time scales are pervasive in science and engineering. In neuroscience experiments, the spiking dynamics of neurons can exhibit variability both within a given trial (fast time scale) and across trials (fast time scale). The behavior of users on social media often exhibits interesting dynamics within a day (fast time scale), as well as dynamics across days of the year (slow time scale).

I propose a separable two-dimensional (2D) random field (RF) model of multiscale stochastic processes whose dynamics a different scales obey a certain separability condition. I term such processes separable multiscale processes (SMPs) and propose efficient algorithms for estimation, inference and optimization in the separable 2D RF model. I demonstrate this model on data collected from neurons in the anterior cingulate cortex (ACC) in an experiment designed to characterize the neural underpinnings on the observational learning of fear in mice.