A Bayesian approach for inferring neuronal connectivity from calcium fluorescent imaging data

TL;DR

This paper introduces a Bayesian method using hidden Markov models and Monte Carlo algorithms to infer neural connectivity from calcium imaging data, demonstrating accurate results in simulated realistic networks.

Contribution

It presents a novel Bayesian inference framework with efficient sampling algorithms for reconstructing neural circuits from indirect calcium imaging signals.

Findings

Accurately infers network connectivity in simulated realistic neural networks.

Incorporates prior knowledge to improve estimation accuracy.

Demonstrates computational feasibility for large-scale networks.

Abstract

Deducing the structure of neural circuits is one of the central problems of modern neuroscience. Recently-introduced calcium fluorescent imaging methods permit experimentalists to observe network activity in large populations of neurons, but these techniques provide only indirect observations of neural spike trains, with limited time resolution and signal quality. In this work we present a Bayesian approach for inferring neural circuitry given this type of imaging data. We model the network activity in terms of a collection of coupled hidden Markov chains, with each chain corresponding to a single neuron in the network and the coupling between the chains reflecting the network's connectivity matrix. We derive a Monte Carlo Expectation--Maximization algorithm for fitting the model parameters; to obtain the sufficient statistics in a computationally-efficient manner, we introduce a specialized blockwise-Gibbs algorithm for sampling from the joint activity of all observed neurons given the observed fluorescence data. We perform large-scale simulations of randomly connected neuronal networks with biophysically realistic parameters and find that the proposed methods can accurately infer the connectivity in these networks given reasonable experimental and computational constraints. In addition, the estimation accuracy may be improved significantly by incorporating prior knowledge about the sparseness of connectivity in the network, via standard L$_1$ penalization methods.