Real-Time Variational Method for Learning Neural Trajectory and its
  Dynamics
Matthew Dowling Yuan Zhao Il Memming Park
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 alternatives to
give immediate feedback to experimentalists, and enhance experimental design,
they have received markedly less attention. In this work, we introduce the
exponential family variational Kalman filter (eVKF), an online recursive
Bayesian method aimed at inferring latent trajectories while simultaneously
learning the dynamical system generating them. eVKF works for arbitrary
likelihoods and utilizes the constant base measure exponential family to model
the latent state stochasticity. We derive a closed-form variational analogue to
the predict step of the Kalman filter which leads to a provably tighter bound
on the ELBO compared to another online variational method. We validate our
method on synthetic and real-world data, and, notably, show that it achieves
competitive performance