Graphical Models and Dynamic Latent Factors for Modeling Functional Brain Connectivity

Abstract

With modern technology, the activity of thousands of neurons in the brain can be recorded simultaneously. Such data can potentially shed light on how neurons communicate with one another. These neuronal interactions are often viewed under the framework of functional connectivity, which is defined as the statistical dependence between recorded neuronal activity. Several have proposed to use graphical models to estimate functional connectivity between neurons directly from neuronal recording data. However, one challenge that can arise from this type of data that is not addressed by a traditional graphical model is the influence of dynamic latent brain states on recorded neuronal activity, as the neurons recorded in one experimental session constitute only a small subset of all the neurons in the brain. These latent states should be accounted for to get a more accurate estimate of functional connectivity. In this paper, we introduce two models, the dynamic mean operator (DYNAMO) and the dynamic covariance operator (DYNACO) conditional Gaussian graphical models, to infer functional connectivity from neuronal activity data after adjusting for dynamic latent brain states. We apply the DYNAMO and DYNACO models to a variety of simulation studies and demonstrate their superior performance over traditional, unconditional graphical models.