Sparse Bayesian identification of synaptic connectivity from multi-neuronal spike train data

Introduction: Recent progress in neuronal recording technique allows us to record spike events simultaneously from a majority of neurons in a local circuit. Here we propose a method for identifying synaptic connectivity from multi-neuronal spike train data based on a electrophysiological neuron model and statistical inference.

Method: The method assumes that spikes are generated from stochastic leaky integrate-and-fire (LIF) neurons [1] connected with multi-exponential postsynaptic current functions. The model is a special class of linear-nonlinear-Poisson (LNP) models and the parameters can be fitted to spike train data by maximum likelihood estimation (MLE) [2]. For a network of n neurons with k postsynaptic current functions, the number of parameters is n²(k+1)+n, which makes MLE prone to over-fitting as the number of recorded neurons increases. To overcome this issue, we develop a Bayesian estimation algorithm with a hierarchical prior that promotes sparseness of effective connection parameters. In the algorithm, the prior distribution of the model parameters is given by a Gaussian distribution with zero mean vector and diagonal covariance matrix, in which each non-zero element is regarded as a independent random variable distributed according to a Gamma distribution. All the random variables in the hierarchical model are identified as the maximum a posteriori (MAP) estimator, which is computed by the expectation-maximization (EM) algorithm combined with the Newton-Raphson method. After the parameter fitting, three types of synaptic connectivity (excitatory, inhibitory, or none) are finally identified based on the maximum amplitude of spike response curves reproduced by the model.

Results: The method was applied to two synthetic benchmarks. First, the spike train data were generated from a network of n=6 stochastic LIF neurons with 4 excitatory and 4 inhibitory connections and the reproducibility of the model parameters and the spike response curve were tested. The proposed Bayesian algorithm could achieve smaller variance of estimated model parameters and reproduced the spike response curves better than the MLE method. In the second benchmark, spike train data were generated from a network of n=15 Hodgkin-Huxley type neurons with 50 excitatory and 25 inhibitory connections and the reproducibility of the types of synaptic connection was tested. According to the ROC (receiver operating characteristic) analysis, the method could estimate three types of synaptic connectivity with a high classification precision (AUC score > 99% in average for our data set).

References

1. Shinomoto, S. (2010). Fitting a stochastic spiking model to neuronal current injection data. Neural Networks, 23, 764-769.
2. Paninski, L. (2004). Maximum likelihood estimation of cascade point-process neural encoding models. Network-Computation in Neural Systems, 15, 243-262.