The Exponential Family Variational Kalman Filter for Real-time Neural Dynamics

Latent variable models have become instrumental in computational neuroscience for reasoning about neural computation. This has fostered the development of powerful offline algorithms for extracting latent neural trajectories from neural recordings. However, despite the potential of real-time algorithms to give immediate feedback to experimentalists, and enhance experimental design, they have received markedly less attention compared to their offline counterparts. We introduce the exponential family variational Kalman filter (eVKF), an online recursive Bayesian method aimed at simultaneously inferring latent trajectories and learning the underlying dynamical system. eVKF works for arbitrary likelihoods and utilizes the constant base measure exponential family to model the latent state stochasticity. Our closed-form variational analogue to the \emph{predict} step of the Kalman filter leads to a provably tighter evidence lower bound (ELBO) compared to previous methods. With constant computational complexity per step, on the order of milliseconds, eVKF is well suited for fine resolution real-time applications. Our method can decode hand position during a monkey reaching task comparatively well to the offline reference method even though eVKF only processes the data once, in a sequential fashion. We believe eVKF will help to advance the development of online inference algorithms that are capable of learning non-Gaussian, nonlinear dynamics, and open up possibilities of perturbing actual neural systems in real-time to better understand the underlying computation.