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

### Yuriy Mishchencko, Joshua Vogelstein, and Liam Paninski

In press, Annals of applied statistics

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 L1
penalization methods.

Preprint (pdf, 700K) | Liam Paninski's home