Real-Time Variational Method for Learning Neural Trajectory and its Dynamics

TL;DR

This paper introduces eVKF, an online variational Bayesian method for real-time neural trajectory inference and dynamical system learning, enabling immediate feedback in neuroscience experiments.

Contribution

The work presents the first online recursive Bayesian algorithm for simultaneous neural trajectory inference and dynamical system learning applicable to arbitrary likelihoods.

Findings

eVKF achieves competitive performance on synthetic data.

It provides a tighter ELBO bound than existing online variational methods.

Validated on real-world neural data.

Abstract

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