Title: GP CaKe: Effective brain connectivity with causal kernels,
Abstract: A fundamental goal in network neuroscience is to understand how activity in
one region drives activity elsewhere, a process referred to as effective
connectivity. Here we propose to model this causal interaction using
integro-differential equations and causal kernels that allow for a rich
analysis of effective connectivity. The approach combines the tractability and
flexibility of autoregressive modeling with the biophysical interpretability of
dynamic causal modeling. The causal kernels are learned nonparametrically using
Gaussian process regression, yielding an efficient framework for causal
inference. We construct a novel class of causal covariance functions that
enforce the desired properties of the causal kernels, an approach which we call
GP CaKe. By construction, the model and its hyperparameters have biophysical
meaning and are therefore easily interpretable. We demonstrate the efficacy of
GP CaKe on a number of simulations and give an example of a realistic
application on magnetoencephalography (MEG) data.