Scalable inference of neural dynamical systems

Fluorescent calcium imaging provides a potentially powerful tool for inferring connectivity in large neural circuits. However, a key challenge in using calcium imaging for connectivity detection is that current systems often have a temporal response and frame rates that can be orders of magnitude slower than the underlying neural spiking process. Bayesian inference methods based on expectation-maximization (EM) have been proposed to overcome these limitations, but are often computationally demanding since the E-step in the EM procedure typically involves state estimation for a high-dimensional nonlinear dynamical system. In this work, we propose a computationally scalable method based on a hybrid of loopy belief propagation and approximate message passing (AMP). The key insight is that a neural system as viewed through calcium imaging can be factorized into simple scalar dynamical systems for each neuron with linear interconnections between the neurons. Using the structure, the updates in the proposed hybrid AMP methodology can be computed by a set of one-dimensional state estimation procedures and linear transforms with the connectivity matrix. The method extends earlier works by incorporating more general nonlinear dynamics and responses to stimuli.