Abstract
Neurons form complex networks that evolve over multiple time scales. In order to thoroughly characterize these networks, time dependencies must be explicitly modeled. Here, we present a statistical model that captures both the underlying structural and temporal dynamics of neuronal networks. Our model combines the class of Stochastic Block Models for community formation with Gaussian processes to model changes in the community structure as a smooth function of time. We validate our model on synthetic data and demonstrate its utility on three different studies using in vitro cultures of dissociated neurons.
Highlights
In order to understand the temporal dynamics of in vitro neuronal networks under various experimental conditions, we present here a statistical model that explicitly captures both the underlying structural and temporal dynamics of neuronal networks on multi-electrode arrays (MEAs)
We propose an extension of the Stochastic Block Model (SBM), called Temporal Stochastic Block Model (T-SBM), that performs inference on longitudinal network data, inferring the community structure of the graphs under study as well as the changes in the graphs over time
The T-SBM accurately inferred the true parameters in the synthetic data, namely the parameters of the covariance functions and the β coefficients associated with each pair of communities
Summary
Temporal Stochastic Block Model (T-SBM)We propose an extension of the SBM, called T-SBM, that performs inference on longitudinal network data, inferring the community structure of the graphs under study as well as the changes in the graphs over time. In the T-SBM we assume that the community assignment of each node is fixed across all time points but that the relationships across communities may change over time. An interpretation of this set of assumptions is that, once formed, the physical connections among neurons do not change. It is not clear how to compare communities across time without some post-processing community disambiguation—which is a nontrivial problem. Such longitudinal study is straightforward with the T-SBM. Because of constraints imposed by the Gaussian process as well as because of the fact that the temporal model is trained on more data, it is more robust to noise than the static model and less prone to overfitting
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