Scalable Inference for Neuronal Connectivity from Calcium Imaging

TL;DR

This paper introduces a fast, scalable Bayesian inference method combining loopy belief propagation and approximate message passing to infer neural connectivity from calcium imaging data, overcoming computational challenges of existing methods.

Contribution

The authors develop a novel hybrid AMP algorithm that efficiently estimates neural states and connectivity from calcium imaging, enabling analysis of large neural circuits.

Findings

Achieves accurate connectivity inference in large neural networks

Significantly reduces computation time compared to MCMC-based methods

Demonstrates effectiveness on realistic neural network simulations

Abstract

Fluorescent calcium imaging provides a potentially powerful tool for inferring connectivity in neural circuits with up to thousands of neurons. However, a key challenge in using calcium imaging for connectivity detection is that current systems often have a temporal response and frame rate 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 fast method for the state estimation 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. This yields a computationally scalable method for inferring connectivity of large neural circuits. Simulations of the method on realistic neural networks demonstrate good accuracy with computation times that are potentially significantly faster than current approaches based on Markov Chain Monte Carlo methods.